unit 1 - pbworks 1... · review 2.1-2.4 test 2.1-2.4 29 30 oct 1 2 3 section 2.5 section 2.6...

Geometry PreAP/GT

Unit 1

Foundations of Geometry

This unit focuses on an introduction of geometry including vocabularyand skills, such as constructions that we will use to explore Geometry

for the rest of the year. Students will build on the foundation of whatthey have learned about Geometry and Algebra from previous years andconnect their prior knowledge to new concepts in math. Students will

also explore the differences between Euclidean & non-EuclideanGeometry.

• Have I seen this before? How does that connection help me in thissituation?

° How are relationships used to find measurement?° How do I show that I understand the mathematics in this situation?° How does the real world relate to geometry? How is it used in the real

world?

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY August 25 26 27 28 29

WELCOME!!!

Rules & Procedures

HW: p. 875(2-36 evens)

Algebra Skills

Assessment

Simplifying Radicals

HW: Simp. Rads. WS #1

Section 1.1 Point, Line, Plane

HW: WS 1.1C (2-32 even)

Challenge (2-12even)

Section 1.1 Point, Line, Plane

HW: WS 1.1C (2-32 even)


Section 1.2 Segments & Congruence

Construct/Copy a line

HW:WS 1.2C (2-30even)

Challenge (2-8 even)

Sept 1 2 3 4 5

NO SCHOOL

Section 1.3 Midpoint & Distance

Formulas

Construction – Midpoints

HW: WS 1.3C (2-32even)


Section 1.4 Measure & Classify Angles

Construct an

angle/angle bisector

HW:WS 1.4C(12-28 even)

Challenge (1-11)

QUIZ 1.1-1.3

w/Algebra

HW: Solving Systems of

Equations WS

Section 1.5 Angle Pair Relationships

HW:WS 1.5C(2-42 even)

Challenge (2-12 even)

8 9 10 11 12

Section 1.6/1.7 Polygons, Area, Perimeter

HW: WS 1.6C &Challenge

WS 1.7C & Challenge

Multiples of 3 on all WS’s

QUIZ 1.4-1.7

HW: Cumulative Rev.

(1-33)

Activity Day

HW: TBA

Activity Day

HW: TBA

QUIZ

Constructions

HW: TBA

15 16 17 18 19

Chapter 1 Review

CW: Review Activity

HW:WS Ch. 1 Prac. Test C

STUDY!!!

TEST

CHAPTER 1

HW: Algebra Review WS:

Binomials and Factoring

Section 2.1/2.2 Section 2.1/2.3 Section 2.1-2.3

22 23 24 25 26

Section 2.4 QUIZ 2.1-2.3 Activity

Proofs

Review 2.1-2.4 TEST 2.1-2.4

29 30 Oct 1 2 3

Section 2.5 Section 2.6 Section 2.7 CUMULATIVE

TEST

Early Release

Activity

Proofs

All assignments are subject to last minute changes!!!!

1st Six Weeks 2014-2015

Solving Linear Equations kÿ"7

To solve a linear equation, you isolate the variable,

Add the same number to each side of the equation,

Subtract the same number from each side of the equation.

Multiply each side of the equation by the same nonzero number,

Divide each side of the equation by the same nonzero number,

Solvethe equation: a. 3x- 5 = 13 b. 2(y- 3) =y+ 4

a, 3x- 5 = 13

3x-5+5=13+5 Add 5.

3X = 18 Simplify,

3_xx = 18 Divide by 3,3 3x = 6 Simplify,

C//£tÿ/( 3x- 5 = 133(6) - 5 _2 13

13 = 13 /

b. 2(y-3)=y+4

2y-6=y+4

2y-y-6=y-y+4

y-6=4

y-6+6=4+6

y= 10

¢tlF.¢K 2(y- 3) = y + 42(10-3)_210+4

14 = 14 ¢"

Distributive Property

Subffact

Simplify,

Add 6.

Simplify.

Solve the equation.

1. x-8=23

a4.-g=7

7. -4.8 = 1,5z

10. 7(y- 2) = 21

13. 2c+3=4(c- 1)

16, 6),_2=10

19. 2c-8=24

22. -4k + 8 = 12 - 5k

25. 12(z + 12) = 152

28. 5(3t- 2) = -3(7 - t)

1.b.8=lO31,ÿ

34. 9-2X=x7

2, n+ 12=0

2 265. ÿr=

8, 0=-3x+12

11, 5=4k+2-k

14. 9- (3r- 1)= 12

17. w-8-43

20. 2,8(5 - t) = 7

23. 3(z-2)+8=23

26, 2.3.14. r = 94,2

29, 20a - 12(a - 3) = 4

32. 4x+ 12_3x_52

35. 23 - llc _ 5c7

t

3. -1.8 = 3y

46. -ÿt = -8

9, 72= 90-X

12, 4/z+1=-2n+8

15. 12m + 3(2m + 6) = 0

18, -1(12 + h) = 7

21. 2-c=-3(2c+ 1)

24, 12 = 5(-3r + 2) - (r- 1)

27, 3.1(2f+ 1,2) = 0,2(f- 6)

30, 5,5(h - 5,5) = 18,18

10+ 7y_ 5-y33, 4 3

36. 4n - 28 _ 21z3

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Skills Review Handbook 875•-.•'


Ex.1) 4ÿ Ex.2) 3ÿoo

Ex.3) 2,fÿ - 5,fi44 Ex.4) 6,Jÿ + 7,f5

Ex.5) -9qr27 + 6ÿ Ex.6)

Ex.7) ÿ Ex.8) Ex.9)


Simplify each square root.

1. ,fag 2. ,/ÿ

4. 4ÿ 5. 424ÿ 6. 4ÿ

7. 2496 8. 4 ,!7-g 9. 6 -4"ff

lO1

11.

113.

114.

19. 4ÿ/ff + 3vr7 20. 2"f6 - "v!-6 2!, ÿ +4"4ÿ

22. 5ÿv/'3 + 3"qr3 + 2 23. ,fff + ÿ/5-0 + 2",Q 24. 4ÿ-d- x/-ÿ +',/5

25. ,!ÿ-9qr2 26. 5-4'ÿ+6,ÿ-2-,/ÿ 27.2.f8--0-6,/1-8+ 5-,/ÿ

Unit 1 Essentials of Geometry (1.1)

Notes 1.1- Points, Lines, & Planes

- points that on the

Picture:

- points that on the

Picture:

/ÿÿ11 it takes is for point

f within the set of points to bethe line to .be considered

EX 1: Find the coordinates of three points that lie on the graph of y = 3x+5 and one point that doesn'tlie on the line.

EX 2: Do points R(4, 8) and S(-3, -7) lie on the line with the equation y = 2x - 1?

Vocabulary:

Undefined Terms - no formal but its

- an in space and is

by aPicture:

Written as:

- collection of along a

extending in directions.

Picture:Written as:

surface extending in all directions.

Written as:Picture:

- Points that in the

Picture:

- Points that lie in the

Picture:

it takes is for point'ÿÿ

n the set of points to

of the plane to be

ered be . ÿ

Defined Terms - terms that can be

such as

using known

or

- part of a line

all on the line

of

the endpoints.

and

Picture:

Written as:

Written as;

- part of a line with

in the

NOT be written as . Theÿÿ

int is always the first letter

I written in the notation for a ray. The )direction the ray is pointing is always /

2nd letter written

endpoint that

direction.

Picture:

If point C Jies on A--Bbetween A & B, then C--Aand C-ÿare opposite rays.

Picture:

- two lines that at exactly

point.

Picture:

- two lines that to form angles.

Notation forPicture:

Line AB is perpendicular to line CD

- two lines that intersect.

Notation for

Picture:

Line AB is parallel to line CD

Thinqs to remember: Picture:

lines intersect at a

Line m intersects line k at point F

Picture:

A and a intersect at a

Line k intersects plane A at point B

Picture:

planes intersect at a

Plane M and plane C intersect at line AB

EXAMPLE: Finish the sketch.

line in the plane line not in the plane

./" .............. /

line intersects at one point

, ' ÿ.._ÿ_o

Name Date

Practice CFor use with #a#es 2-#

'ÿ.ÿ-,

In Exercises 1-16, use the diagram.

1. Give five other names for AB.

2. Name four sets of three points that are collinear.

3. Name three points that are ooplanar with bothplane K and plane L,

4. Name all points that are not eoplanar with pointsA, B, and H.

5. Give another name for CG.

6. Name all rays with endpoint G.

7. Name four pairs of opposite rays,

8. Give another name for FB.

9. Are points.4, G, and Ncollinear?

10. Are points A, G, andN coplanar?

1 I. Are points C, D, and G collinear?

12. Are points C, D, and G eoplanar?

13. Name the intersection of AB and MN.

14. Name the intersection of C"D and plane ABH.

15. Name the intersection of plane K and plane L.

16. Name the intersection of ÿ"ff and plane K.

I K

', ;F

Sketch the figure described.

17. Three lines with only twopoints of intersection

19. Two rays that intersect at their endpoints 20.

18. Two planes that do not intersect

Two collinear rays that do not intersect

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Geometry10 Chapter 1 Resource Book

Name Date

ss0. Practice C ÿoÿtÿ.ÿ1.1 For use with pages 2-#

You are given an equation of a line and a point. Use substitution todetermine whether the point is on the line.

21. y=3x+7;A(2,13) 22. y=4x-3;A(5,17) 23. 2y=-3x-9;A(-l,-3)

24. 5x + 4y = 28; A(4, -2) ZS. 6), - 7x = 8; A(6, 4) 26. -2x - 9), = -20; A(-8, 4)

Graph the inequality on a number line. Tell whether the graph is asegment, a ray or rays, a point, or a linÿ

27. x>6 28. x<--lO 29. --5ÿxÿ3

,I I I I I I I I Iÿ ÿ1 I I I I I I I I' 11[11111111ÿ

30. X>4orx<7 31. x>Oorx<--2 32. x2<O

In Exercise 33-35, use the following information.

Perspective Drawing A perspective drawing is drawn using vanishing points, asdescribed in the text. The figure below is a perspective drawing of a garage,

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33. Draw the lines necessary to locate the two vanishing points,

34. Using the two vanishing points, draw the lines necessary to show the hidden lines of

the garage,

35. Using heavy dashed lines, draw the hidden lines of the garage.

GeometryChapter 1 Resource Book 11

Name Date

Challenge PracticeFor use with pages 2-8

lw

2,

-%tÿ

®

Name 15 different rays in the diagram atthe right, Then name 3 pairs of opposite rays,

Draw four noncollinear points A, B, C, and D.Sketch A'--D and add_.ÿa point Eo._q£ AD, Sketch ÿ andadd a__ÿoint F on EB, Sketch FC and add a point Gon FC, Sketch plane AEF,

In Exercises 3-8, use the diagram at the right.

3. Name the intersection of plane YZT and plane XYT.

4. Name the intersection of'plane WXTand plane YZT.

5. Are points Z, Y, and Wcollinear? Are they coplanar?

6. Name three planes that intersect at point IF.

7. Name three lines that intersect at point Y,

8. Do the planes YXT, WXT, and WVT intersect in one line? y X

In Exercises 9-12, you are given two equations of lines and a point.Do the lines intersect at the given point7 Explain your reasoning.

9. y=5x+l 10. y=-2x+6

y=-5x+l y=3x-4

A(0, ]) A(3, 3)

11. y=x+8 12. y=Zr-5

y=-4x-3 y=3x+ l

A(-2, 6) A(-6,-17)

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Unit 1 Use Segments& Congruence (1.2)

The length of a segment is the between its

° Draw an example of a point that would be between A and C.

mThe measure of AB is written as

** It is the between and • So the measure of a is

the same as the its two endpoints.

Is the distance from A to B different than the distance from B to A? Why or why not?

A postulate is a

The Ruler Postulate:

The numbers on a ruler are a example of a

The between two points on a number line is the

of the difference of the coordinates. It can be found using:

AB=

EX 1:

I t I I I I \\7 t I I I 1! I ! ! T I''lll,,, 11 I I I 1 t ! TI I /-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Distance from X to Y can be written as: OR

EX 2: Find PQ, QR, and PR if P is located at -3, Q is located at 1, and R is located at 6.

Segment Addition Postulate: If Q is P and R, then

If , then Q is P and R.

! /+

small segment ÷ small sÿjmeÿt = big ÿgment

EX 3: Find LM if L is between N and M, NL = 6x - 5, LM = 2x + 3, and NM = 30.

EX 4: Find the measure of MN if N is between M and P, MN = 3x + 2, NP = 18, and MP = 5x.

Conqruence:

Congruent means and is written as

Conqruent segments- segments that have the

!" I , Lengths are equal, segments aFe congruent.

ic: /I\\ D t "is equal i'o" "is congruent iÿo"

congruency marks

EX 5: Use the picture below to find AB if K is between A and B, AK = 2x + 10 and KB = 5x + 4.

f ÿ 8- t

A K B

Name Date

Practice CFor use with pages g-N

Measure the length of the segment to the nearest tenth of a centimeter.

1. A B 2. C D 3. E8 0 . • Q

Find the indicated length,

4. Find G J, 5. Find KL,

- ' I 33.46,7 ÿ 8.6 ÿ ;

K L 21.9 M

6. Find NP,

I ,8o.1 --tN P 37.5 O

Plot the given points in a coordinate plane. Then determine whether theline segments named are congruent.

7. A(0, 4), B(8, 4), C(6, 6), D(6, -2);AB and CD

8, E(-3, -2),/?(-3, 2), G(4, 5), H(4, 9);

EF and GH

--t--l--

Y3q-ÿ .......

1.|--4---6- ......

.L_LL ÿ"

!:ii

10,J(- 1, -5), K(6, 2), L(9, -5), M(6, - 10);

JL and KM

Iii

LLL_

P(-10, 4), Q(-5,

PR and QS9,

1), ÿ(-10,-3), s(-5,-6);

I i - ,- ._T.'.']]]211'- ...... FI . -2 .....

Use the number line to find the indicated distance.

V W X Y Z

-18-16-14-12-10--8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18

aa. VII a2. XY ÿ3. XZ

15. FY 16. WZ 17. WY

E

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Name Date

. ss0, Practice C 0,t;,,0d1.2 For use with pages g-N

In the diagram, points A, B, 17, D, and G are collinear, points E, F, G,/4,and Jare collinear, CD = 10.4, BD = 19.1, GJ = 21.3, BG = 30.6,AB = BC = EF = GH, and DG = FG. Find the indicated length.

19. AB

20. CG

21. AG

22. FG

23, EH E

24. EJ

Find the indicated length.

25. Find LM, 26. Find PQ, 27. Find ST.

I 22- ÿ t 41 I I-ÿ 8x + 9

" ; x+5 ,; 7x-8 3x+ rK x

8._=

'S

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@

Point B is between A and C on A--C. Use the given information to write anequation in terms of x. Solve the equation. Then find AB and BC.

28. AB = 7x + 2 29. AB = IOx + 4 30. AB = 4x + 3BC= 2x- I BC=4x- 3 BC=Bx- 11

AC = 64 AC = IZÿ: + 16 AC = lO.5x + 4

31, Marathon A marathon is being planned in your city,The course for the race is through different parts of thecity as shown in the graph, The race starts at point A andthe finish line is at point F. The distance is in miles.

a. How many miles is the entire race?b. How many miles is it from the start of the race to point C?

c. How many miles is it from point D to the finish line?

d. How many miles would be eliminated from the race if therunners were told to turn left at point (6, 4,8) and then headstraight for the finish line?

'ÿ2. ÿ, ,ÿ ÿ

tNÿ-=- <*mk,.ÿ :


Name Date

Challenge PracticeFor use with pages 9-14

1,

2,

In the diagram at the right, AB = CD. Use the SegmentAddition Postulate to show that AC = BD.

In the diagram at the right, QR -ÿ ST-ÿ UV and RS ÿ TU.Use the Segment Addition Postulate to determine whatother segments must be congruent.

In Exercises 3-5, let A, B, C, 17, and Fbe five points in the plane.Determine whether the given condition is sufficient to concludethat AD + DE+ FC + CB = AB. Justifyyour answer using theSegment Addition Postulate and/or by malting a sketch.

3. D is between A and C, and F is between D and B.

4. Fis between D and C, A is between D and F, and B is between F and C.

5. C, D, and F are all between A and B.

:-':2"-?

g%:,!

6m In the diagram, A"-fi ÿ GE, CD ÿ CB, CH ÿ HI = ID,1CE=ÿAE, AB=CB= 12, DG=8, andCE=6.

a. Find the lengths of all the segments in the diagram.

b. Suppose you choose one of the segments at random.What is the probability that the measure of the segmentis greater than 8'? Explain how you obtained your answer.

O

F B

G E

LM = x2

MN = x2 + 9x

LN = 56

in Exercises 7-9, point/Y/is between /. and/Von L/Iÿ. Use the giveninformation to write an equation in terms of x. Solve the equation(disregard any answers that do not make sense in the context ofthe problem). Then find/;////and/Yÿ/ÿ.

7. LM = x2 8. LM = .\'2 - 6x 9.

MN = x MN = xLN = 12 LN = 50

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Unit 1 Use Midpoint & Distance Formulas (1.3)

What is the coordinate of the midpoint XY?

____________ means to __________ in ____________.

EX 3: If P is the midpoint of CD and PC = x and PD = 5x – 4, find the value of x and the measure

of CD.

EX 4: L is between H and Z. Q is the midpoint of HL. LZ is twice as long as HQ. HL = 7x – 5

and HQ = x + 5. Find HQ and HZ.

oÿ"ÿordinate plane midpoint formula:

The coordinates of the of a segment whoseendpoints are (Xl, yl) and (×2, y2) are

EX 5: The endpoints of R-S are R(1, -3) and S(4, 2). Find the midpoint.

EX 6: The midpoint of RQ in the graph below is P(4, -1).Find the coordinates of R if Q is at (3,-2)

t ÿ t • ) ÿ ÿ ÿ

II f ! I ÿ r iÿ " "

t-i I ÿ ÿ ÿ tt'ÿ F

L..I....L_Lÿ ÿ._ L_.!ÿ._L._L

.EX 7: What happens when you are missing an endpoint?The midpoint of JK is M(-2.5,-1.5). One endpoint is J(-6,13).

Find the coordinates of endpoint K.

EX 8: What is the exact length of segment RS if R(3, 2) and S(-4, 3).

EX 9: Determine if the two segments AB and LK are congruent.

1 3

: ( ,2); (3, )2 4

AB A B 1 1

: ( ,1); (2, )2 4

LK L K

Name Date

Practice CFor use with pages 15-22

Find the indicated length.

1. Line JK bisects L--M at point J. Find JM ifLJ = 23 centimeters.

-- 5 ,2. Line WXbisects YZ at point W. Find YZ if WZ = 9ÿ inches.

3. Point F bisects G-H. Find GH if GF = 147 feet,

4. Point R bisects S--T, Find RTifST = 16.9 meters.

In the diagram, M is the midpoint of the segment. Find the

indicated length.

5. Find MQ. 6. Find UF. 7. Find DE.

4x- I 12x- 17 21x- 13 10x+ 31 5x- 6 2x+ 5i

E

Find the coordinates of the midpoint of the segment with the

given endpoints.

8. ,4(6, -3) and B(10, 5) 9. M(14, 7) and/7(-9, 1)

10. Y(-13,8)andZ(2,-lO) 11. C(- 5, -17) and D(-18,12)

Use the given endpoint R and midpoint M of R---S to find the coordinates of

the other endpoint $.

12. R(8,0),M(4,-5) 13. R(7,-17),M(-2,3)

14. R(-6, -9), M(8, -5.5) 15. R(11, -16), M(-3.5, -9.5)

Find

16.

18.

the length of the segment. Round to the nearest tenth of a unit,

-- ÿ ...... S .... 17, -1-F"F- y-q- .....

s/-=,,ou]

;219,

! Vÿ-r-r-r-ÿ-qÿCLT_ÿ

-t--I--'N(- 1, 2)ÿi-l'-i -!

--F-t ¥ÿ'<-4,-4 ÿ--I-L..J._.L._]._ .L ....... L_I ... L..I

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Name D ate

LEssa. l Practice C eo.ti...d1,3 For use with pages 15-22

Find the length of the segment. Then find the coordinate of the midpoint

of the segment.

20. J K 21. P Q1,, I¢,,,, ,, I II;€',= ÿ1 lÿl I I If',', I€',ÿ

-20 -16 -12 -8 -4 0 4 -40 -30 -20 -10 0 10 20

The endpoints of two segments are given. Findwhether the segments are congruent.

2z. Zÿ: A(7, 2), B(o, -3)C--D: C(-4, 12), D(-1, 4)

hÿ7

24. ÿ:K(-lO, 8),L(2, 7)M--N: M(14, -4), N(5, 4)

each segment length, Tell

23. RS: R(5, 6),S(II, -2)--ÿ: ÿ-7, 9), u(3, 9)

zÿ. o'-P: 0(-6, ÿ2), P(o, 7)

Q"-'R: 0(8, -5), R(12, 2)

In Exercises 26-29, find the distance between the two cities using theinformation in the table. Each data point is from a coordinate system usedfor calculating long-distance telephone rates. Round your answer to the

nearest whole unit,

Buffalo, N¥ (5075, 2326) Omaha, NE (6687, 4595)

Chicago, IL (5986, 3426) Providence, RI (4550, 1219)

Dallas, TX (8436, 4034) San Diego, CA (9468, 7629)

Miami, FL (8351, 527) Seattle, WA (6336, 8896)

26. Buffalo and Miami 27. Chicago and San Diego

28. Dallas and Seattle 29. Omaha and Providence

In Exercises 30-32, use the map.

30. Find the distance between each pair of towns,Round to the nearest tenth of a mile,

31. Which two towns are closest together?Which two towns are &rthest apart?

32. The map is being used to plan a 36-mile bicyclerace. Which of the following plans is the best routefor the race? Explahÿ.A. Dunkirk to Clearfield to Allentown to Dunkirk

B. Dunkirk to Clearfield to Lake City to Allentownto Dunkirk

C. Dunkirk to Lake City to Clearfield to Dunkirk

D. Dunkirk to Lake City to Allentown to Dunkirk

8,=_

...... r .......... ÿ ..... ,

:::::::::::::::::::::::::::Lake C ÿ_]__

-'-[ (- 1ÿ6)"ÿ:2: Allentown

SL-! (7, 0). ! :Distance (mi)

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Challenge PracticeFar usa with pages 15-22

I, Use the Midpoint Formula three times to find the three points that divide AB withendpoints A(xt, Yl) and B(x2, Y2) into four equal parts.

2. Use the result of Exercise I to find the points that divide AB with the givenendpoints into four equal parts,

a. A(I, -2), B(4, -1)

b, A(-2, -3), B(0, 0)

3. Explain how you can use the Distance Formula and the Segment Addition Postulateto determine whether three points A, B, and C in a coordinate plane are collinear.

In Exercises 4-7, tell whether the three given points are collinear.

4. A(2, 6), B(5, 2), C(8, -2) 5. A(2, 3), B(2, 6), C(6, 3)

6. A(-2,-2),B(I, 1), C(7, 5) 7. A(-I, -8),B(4,7), C(6, 13)

In Exercises 8-11, use the following information to find the distancebetween A and Bend the coordinates of the midpoint of AB.

In a three-dimensional coordinate system, the distance between two points A(Xl, Yl' zl)

and B(x2, Y2, z2) is

AB = ÿ/(x2 - Xl)2 + (Y2 - Yl)2 + (z2 - zt)2'

In a three-dimensional coordinate system, the midpoint M of A-B with endpoints

A(Xl, Yl, zl) and B(x2, Y2, z2) has coordinates

" ' 2 '

8. A(3,2,5) 9, A(4,1,9) 10. A(-3,5,5) 11.

B(7, 4, 8) B(2, 1, 6) B(-6, 4, 8)

1 2. (0, 45) (30, 45) (60, 45)Floor Plan An engineer is designing a department store.The diagram at the right shows the first floor of the store,The store is to have one escalator going up to the secondfloor and one escalator going down to the first floor fi'omthe second floor. Each escalator is supposed to beequidistant fi'om four of the six store entrances. The labeledpoints shown represent the store entrances.

a. Where should the escalators be placed'?

b. How far apart should the escalators be placed?

rain

(0, 0) (30, 0) (60, 0)

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Unit 1 Measure & Classify Angles (1.4)

**Remember:

directions along the same line.

are rays that share an and extend in

IH G

o iI

IAn is formed by 2 'with a endpoint+

Ai -i Ill I II III I I II Illl

B / .....

BA and BC are the__ of the angle.

B is the common endpoint called the ..............

C

Name angles with three letters, vertex in the middle.

C

. D

P

Angles are measured in ........... .....

A, +-, can be used to find the measure of an angle.

Anÿÿgle Addition Postulate:

If P is the interior of < RST, then

P

S

EX !: Given that m< LKM : 145°, find m< LKN and m< MKN.

L (2x + 10)9 Ni - 3)°

K M

Classifying Angles

- ' A- ÿ A

EX__I.ÿ3: Given that <KLM is a straight angle, find m< KLN and m< NLM.

N/(10x - 5)°ÿ4x + 3)°

LK M

EX 4: Given that < EFG is a right angle, find m< EFH and m< HFG.

<ABC ~<AFG"iÿ congruent to"

-angles that have the

m< A BC = m< A FG"is equal to'ÿ

meQsure.HoW would you mark theangles to show congruency?

An is a ray that divides an angle into two angles.

Congruency marks jÿfor anglesÿB_L

D

BC bisects < ABD< ABCN-- < CBD

EX 5: XB bisects <AXC, m< DXC = 64°. Find x if m< AXB = (2x + 6)°.

D × A

EX 6: Using the same picture, find x if m< AXB = (5x - 10)0 and m< CXB = (7x - 46)°.

Name Date


Use a protractor to fÿnd the measure ofthe given angle. Then classify the angleas acute, obtuse, right, or straight.

1, Zÿ4FB 2, ZBFD

3, ZAFC 4. ZAFE

Give as many other names as possible for the angle inthe diagram. Tell whether the angle appears to beacute, obtuse, right, or straight.

5. ZHGM 6, ZKLG

H K

7. ZKJM 8. ZJKL

9. ZHML lO. ZGJKM

Find the indicated angle measure.

11. mZNPQ=9--- 12. mZSTU= ?_-2--

R

P Q

13.

Use

14,

mZ YWZ = ?ÿ

X W Y

123'5"ÿZ

the given information to find the indicated angle measure,

Given mZADC = 118°, find mZADB,

/(ÿx = 3)°O C

15, Given mZ EHG = 77°, find mZ FHG.

(13x -ytG

Given that ÿ bisects ZJKL, find the two angle measures not given

in the diagram.

16. ÿ51oN 17. J K 18. 790Mÿj

J M M

• tM " KK [' L

(_ÿ,_=

.1=

:lZ"5

@.ÿ.


Name Date

LESSO. Practice C continued1.4 For use with pages 24-34

Find the indicated angle measure,

19, a° o!420. b°

a o

21. C° ÿ b°/

/22. d°

In each diagram, Bÿ bisects ZABC. Find m/ABC.

23. B 24. ID

4C (5x+ 16)- 23)°

25.

#oÿrj

'so=

@.==

Plot the points in a coordinate plane and draw ZABC. Classify theThen give the coordinates of a point that lies in the interior of the

26. A(I,5),B(2, I), C(6,2) 27.

angle.angle.

,4(-3, -1), B(0, -2), C(4, 2)

!

• I tl't14 I ] , | ÿ"

..... t--t--t- --'

-----1

28. Streets The diagram shows four streetsand their inters__.ecfions, All streets arestraight and CG bisects ./ALE.

a. Which angles are acute? obtuse? right?

b, Identify the congruent angles.e. IfmZDLE = 38°, mZBKE = 153°,

mZ B,/H = 65°, and mZ CMF = 117°,find m.! CLD, mz£ EKF, mZ FJH,/n.! FMG, m / DJF, and/nZDLG,

A Tenth Street


Name Date

B Challenge PracticeFor use with pÿges 24-34

In Exercises 1-4, teli whether the statement is always, sometimes,or nevertrue. Explain your reasoning.

1, A pair of opposite rays form a straight angle.

2. The measures of two acute angles add up to 90°,

3, If C is in the interior of ZADB, then ZADC = Z CDB,

4, Whena ray bisects a straight angle, two congruent acute angles are formed,

In Exercises 5-1 I, use the following information.

D is in the interior of ZBAE, m/BAC = 125°

E is in the interior of L DAF, mL EAC = 95°

F is in the interior of LEAC, ntZBAD = mLEAF = mLFAC

5. Draw a sketch that uses all of the given information.

6. Find mZFAC,

7. Find mZBAD,

8,

9.

10.

11.

12.

Find mZ FA B,

Find m Z DAE,

Find m Z FAD.

Find m Z BAE,

Use a piece of paper folded in half three times and labeled as shown,

L , i cia. Name eight congruent angles.

b. Name eight right angles,o, Name eight congruent obtuse angles,d. Name two angles that share a common vertex and side (but no common

interior points), and combine to form a straight angle,

E

,=_

......

8

@

o


Solving Equations Worlcsheet

Do on own paperSolve for the variable in each problem.

1. 5(3x- 2): 35 1 l(6x + 24)- 20 : -!(12x- 72) 3, 5r-2(2r+8)=16

o 13-(2e + 2): 2(e + 2)+ 3c , 1(8y+4)_17 -1=-ÿ-(4y-8) 6. 12-3(x-5)=21

Solve each system of linear equations.

fx = 3y - 41, [2x- y = 7 1

3b + 2a = 2

-2b+a=8m

r - 2s = 0

4r-3s = 15

t

y- 2x = 0

3x+7y=17

p

5.x-3y = 7

-3x + 16y = 28,

8x + 4y = 6

4x=3-y

f

3x - 4y = 16

5x+6y 148ÿ

7p + 5q = 2

8p-9q=179ÿ

2a + 3b = -1

3a + 5b = -2

10. {3x-2y=105x+3y=4

j'2p + 5q = 911,

[3p-2q 4

f3x - 8y = 1112, [x+6y=8

x + 3y = 313. [2x=-6y-12 f4x - 6y = 1014. [5+3y=2x

3x - 5y = -9

15. [2y=3x+3

Unit 1 Angle Pair Relationships (1.5)

**Remember:

Intersectinq lines - two lines that meet at exactly one point.

Perpendicular lines ( _1_ ) - two lines that intersect to form 900 angles.

Parallel fines ( // ) - two lines that NEVER intersect.

- two angles that share a .vertex and side.

- two angles whose sum is 900

**angles can be named vJlth orÿ letter or number. Youmust use three letters when angles are adjacent andthere is no number.

H

K

Must usÿ 3 lÿtters for this pictureoR

- two angles whose sum is ;1800R

Must use 3 letters for this picture

OR

EX____!1: Find the measure of the complement and the supplement of <1.

m< 1 = 22°

c= s=

J

< I and < 2 are complementary angles and <2 and < 3 are supplementary angles,Given the measures of < t, Find m< 2 and m< 3.

m< 1 = 36°

m< 2 = m< 3 =

Xÿ.ÿ.lÿ: < A and < B are complementary angles. Find the measure of eachangle if m< A = (7x + 21)o and m< B = (9x + 5)°,

m< A= m< B=

.EX 4: < A and < B are supplementary anglesÿ Find the measure of eachangle if m< A = (7x + 21)° and m< B = (9x + 5)°.

m< A = rn< B =

Two adjacent angles are arays. The angles in a linear pair aremeans twoH!!

M K

if their are oppositeangles, Remember pair

< JML and < LMK are a linear pair < PQR and < RQTare a linear pair< PQ5 and < PQR are a iinear pair< RQT and <TQS are a Iinear pair< TQS and < PQS are a linear pair

Two angles are_l__..lif their sides form two.

< i and < 3 are vertical angles

< 2 and < 4 are vertical angles

***Vertical angles are always l!!

EX 5: Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Findthe measure of each angle.

EX 6: ÿandÿintersect at point E. Find the measure of<AEC and < CEB if m< AEC = (12x - 5)° and m< BED = (4x + 19)0*Hint* Draw a picture!!

EX 7: Ray DA bisects the straight angle BDC. Solve for x and y. A

2x +2y x -4y

B

EX 8: Given the following diagram, find x and y.

-12y

24


/1 and Z2 are complementary angles and Z2 and Z3 are supplementaryangles. Given the measure of /1, find m/2 and mZ3.

1. mZl = 43° 2. mZl = 28° 3. mZl = 69.5° 4. mZl = 17.5°

Find m/ABCand m/ CBD.

6° c c

:)okÿ ÿsx+ 91° x+ 171" (14x- 6.Sl + 81°

(11x " " : A B O: :-- A B DA B E

In Exercises 8-15, use the diagram. Tell whether the angles arevertical angles, a linear pair, or neither.

8. ZlandZ2 9. ZI andZ3 5ÿ

10, Z2andZ4 11.. Z4andZ5 1 25 3

12, Z6andZ8 13. /8andZ96 11

14. Z7andZl0 15. Zl0andZll ÿ /8

,ÿ,ÿ ,ÿ-ÿ

#

,=_.g

==

"5

g'N"N

G1

gg

@

16. The measure of one angle is 7 times the measure of its complement. Find the

measure of' each angle.

17. Two angles form a linear pair, The measure of one angle is 15 times the measure ofthe other angle. Find the measure of each angle,

18. The measure of one angle is 47° less than the measure of its supplement, Find the

measure of each angle,

Find

19.

the values of xand/4

o

22.

GeometryChapter 1 Resource Book

......... I20y+ 1)

67

Name Date

L s0. ]Practice C1.5 j For use with psgas 35-41

Tell whether the statement is a/ways, sometimes, or nevertrue.

Explain your reasoning.

ZS. Two vertical angles are adjacent,

26. Two supplementary angles consist of one acute angle and one obtuse angle,

27. An angle that has a complement also has a supplement,

43.

In Exercises 39-42, use the star at the rightand the angles identified to name two pairsof the indicated type of angle pair.

39. Supplementary angles

40. Vertical angles

41. Linear pair

42. Adjacent angles

/A and ZBare complementary angles. Find m/A and mZB.

28. mLA = 5x° 29. mZA = (16x - 13)°

m/B = (17x + 2)° mXB = (2x - 5)°

30. mZA=(4x+31)° 31. m/A=(21x+ 12)°

mZB = (-2x + 44)° mXB = (35x - 6)°

/A and/Bare supplementary angles'. Find m/A and/nXB.

32. mLA = (.'c + 11)° 33. mLA = (gx - 12)°

mXB = (x - 15)° mXB = (24x + 60)°

34. mZA=(-3x+90)° 35. mZA=(9x+28.5)°

mXB = (-5x + 150)° mZB = (-5x + 101,5)°

Tell whether the two angles shown are comp/ementarF, supplementary,

or neither.

"GQ "

Use the star above, Determine the total number of pairs or'vertical angles,Determine the total number of linear pairs. Determine the total number ofpairs of'adjacent angles,

&

z;

==

=g

@z=


Name Date

Challenge PracticeFor use with pages 35--41

1. Let ÿ A and ÿ B be complementary angles and let mÿ A = (2x2 + 35)° andnzÿ B = (x + 10)°. What is (are) the value(s) of x? What are the measures of

the angles?

2. Let ÿ A and ÿ B be supplementary angles and letmÿ A = (x2 + 12x)° andmÿ B = (3x2 + 20)°, What is the value of x? What are the measures of the angles?

3. The sum of the measures of'two supplementary angles exceeds the difference oftheir measures by 116°. Find the measure of each angle.

4. The sum of'the measures of'two complementary angles exceeds the difference of'themeasures of their supplements by 32°. Find the measure of each angle,

In Exercises 5-8, determine whether the statement is true or false.Exp/a/A your reasoning and make a sketch that justifies your answer,

5. Ifÿ AGB and ÿ BGC are adjacent, then the angles form a linear pair,

6. If ÿ ABC and ÿ CBD are a linear pair and if ÿ CBD and ÿ DBE are also a linearpair, then ÿ ABC and ÿ DBE are vertical angles,

7. ]f Z JKL is a right angle and €ÿ JKM is an acute angle, then the angles fonaÿ a

linear pair,

8. If €ÿ JKL and ÿ MKNare vertical angles, then Z NKL is a straight angle,

In Exercises 9-12, find the values of xand yshown in the diagram.

E

.--R

£

ro

@


Unit 1 Classify Polygons (1.6)

A is a closed figure formed by a finite number ofsegments called where each side intersects exactlytwo other sides at their endpointso

Each endpoint of a side is a of the polygon

- no line that contains a side of thepolygon contains a point in the interior of the polygon.

convex poiygon

- a polygon that is not convex. Also called

nonconvex,

concave polygon

EX 1: Tell whether the figure is a polygon. If it is a polygon, tellwhether it is concave or convex.

- all sides

- all interior angles

- both and CONVEX polygon.

: How would you mark the fofJowing polygons to show that they are regular?

Regular Pentagon Regular Hexagon

#of sides

3

4

5

6

7

8

9

10

12

n

Type of polygon

Classifying polygons I

EX3: Classify the polygon by the number of sides. Tell whether thepolygon is equiJateral, equiangular, or regular. Explain your reasoning.

EX 4: Draw a figure that fits the descript{on.

A pentagon that is equilateralbut not equiangular.

A concave heptagon

EX 5: The length(in meters) of two sides of a regular pentagon arerepresented by the expressions 7x - 8 and 4x + 10.

Find the length of a side of the pentagon.

EX 6: Find the x and y values if the three sides of a regular triangle are 10, 2x + y, and 6x - 2y.

B Practice CFor use wtth pages 42-47

Tell whether the figure is a polygon. If it is not, explain why. If it is apolygon, tell whether it is convex or concave.

Classify the polygon by the number of sides. Tell whether the polygon isequilateral, equiangular, or regular. Explain your reasoning,

4"I 7ft

7ft

6.

N

8. The lengths (in meters) of two sides era regular heptagon are represented by theexpressions 1 lx - 32 and 6x - 7. Find the length era side of'the heptagon,

9. The expressions -3x + 67 and 7x - 18 represent the lengths (in inches) of twosides era regular nonagon, Find the length era side of" the nonagon,

10. The expressions 6x + 36,5 and 13x - 54,5 represent the lengths (in feet) of twosides era regular pentagon. Find the length era side of the pentagon,

Draw a figure that fits the description.

11. A convex hexagon 12. A concave heptagon

13. An equilateral octagon that is notequiangular

14. An equiangular octagon that is notequilateral

a::==:2

,.n

g;g

@


]Practice C e.ti..ed1.6J For use with pages 42-47

Tell whether the statement is always, sometimes, or never true.

15. A regular pentagon is concave. 16. A square is a regular polygon.

17. A dodecagon is convex, 18. A triangle is equilateral but not equiangular.

Each figure is a regular polygon. Expressions are given for two sidelengths. Find the value of x.

19. 2x+ 27 20. //Fÿ5x _ 32 21,

- 27 ÿ /4x + 45/xÿ - 3x + 85

x2 + lOx - 19

22, 23. ÿx2 _ 19

4X2 + x- 37

2x2 + 89-x2 + x + 43

24.

x2 + 6x - 7,5

+ 42

#E

==

==

==

'ÿ,

oÿ

@

25.

26.

The vertices of a figure are given below,Plot and connect the points so that theyform a convex polygon. Classify the figure.Then show that the figure is equilateral using algebra,

A(-2, -1), B(-1, 2), C(2, 3), D(5, 2),E(4, -1), F(l, -2) .... !-+-

_L..L..ÿ .....

Envelope Envelope manufacturers fold a specially-shaped piece of'paper to makean envelope, as shown below,

Step I Step 2 Step 3 Step 4

a. What type of'polygon is formed at each step?

b. Tell whether each polygon is convex or concave,c. Explain the reason for the V-shaped notches that are at the ends of the folds,

.ÿ,ÿj ,: ÿ .,, ÿ 2ÿÿ- .,


Name Date

Challenge PracticeFor use with pages 42-#7

In Exercises t-4, draw a figure with the indicated condition.

1. A hexagon with exactly one line of symmetry

2. A hexagon with exactly two lines of symmetry

3. An octagon with exactly two lines of'symmetry

4. A pentagon with no lines of symmetry

In Exercises 5 and 6, plot the points in a coordinate plane. Then determinewhat type of polygon the points form. Is the polygon equilateral? Justify

your answer.

5. A(3, 9), B(6, 9), C(8, 7), D(8, 4), E(5, 4), F(3, 6)

6..4(6, 6), B(9, 4), C(8, 1), 9(4, 1), E(3, 4)

In Exercises 7-9, the figure shown is a regular polygon. Find the values

of xand y.

':'ÿ"-ÿ.ÿ-ÿ

7, 4//- X "12x- 4

X+F

9. Bx- 4y

3//- x+ 8'ÿ2x-

x+ //

10, Show that the diagonals of'the quadrilateral in the figure intersect at their midpoints,

IY (b,d

I(o, o)

(a+ b,ÿ

(a, o) X

o

@


Unit 1 Perimeter, Circumference and Area (1.7)

Square Rectangle Triangle Circle

Area

Perimeter

EX 1: The width of the in-bounds portion of a singles tennis court is shown. Find theperimeter and area.

78 ft

27 ft

EX 2: The smallest circle on an Olympic target is 12 cm in diameter, Find the approximateand exact circumference and area of the smallest circle.

EX 3: The area of a triangle is 578 cm2. Its base is four times the length of its height.Find the height and base of the triangle.

EX 4: Convert the following:

10 m2 - cm2

4 ft2 = in2

20 ft2 - i yd2


Find the perimeter and area of the figure. Round decimal answers to thenearest tenth.

• ."'ÿ",-""-;.ÿ"ÿ'ÿ-ÿ;'.::';'.'ÿ ':"=ÿ ÿ " in,

24 m iiÿi).iÿi-::ijiÿ:iÿiÿiÿ..':lÿ! 6,9 em

13.5 cm 16 in.

Find the circumference and area of the circle. Round your answers to thenearest tenth.

4.

7. A triangle has a base of 33 yards and a height of56 yards, Sketch the triangle and find its area.

8. A circle has a radius of'20,2 inches, Sketch thecircle and find its area, Round your answer tothe nearest tenth,

Find the perimeter of the figure. Round decimal answers to the nearesttenth of a unit.

Copy and complete the statement,

lZ. 47cma= ?__2_mÿ 13.

15. 38mmÿ= ÿ.__ÿcma 16.

18. 51,6 ft2 = ? in.2 19.

11.

:} i ....... ........ Y 4

63 in 2 = __7__ ft2 14. 19 yd2 = 9 ft2

2000m2=__2_kin2 17. 85fl2= .9 yd2

92,4km2=_2? m2 20. 108,9m2= ?_2__cm2

€..)._=

gAo

tÿ

g

@

,5

21. A triangle has a base of 71 inches and a height of 60 inches, Find its area in squareyards, Round your answer to the nearest tenth,


:. ÿ==: ÿ--- ÿ-ÿ,:ÿF;ÿiÿ ÿ 7=ÿÿ ,7ÿ

Name Date

Practice C e.ti, eed1,7 For use with pages 48-56

Use the information about the figure to find the indicated measure,

22. Perimeter = ll7 m 23. Area = 345 cm2 24. Area = 826.5 ft2

Find the length $. Find the base b. Find the height It.

,t

19m

50 cm

b

h

34 ft 38 ft

>%

ca.E

._=

@

<.5

28. Shingles You are buying shingles for a roof. Each bundle ÿ:of shingles will cover 33 square feet. The reef consists oftwo rectangular parts, and each is 60 feet by 36 feet.How many bundles of shingles do you need?

25. The perimeter of a rectangle is 690 inches, and its length is 213 inches. Find the

width of the rectangle.

26. The area era rectangle is 144 square meters. The length of the rectangle is threetimes its width. Find the length and width of the rectangle.

27. The area era triangle is 578 square centimeters. Its base is four times the length ofits height. Find the height and base of the triangle.

29,

30,

Irrigation A new irrigation system has been installed. Each irrigation armcovers a circular region with a radius of 45 feet. How many square feet will8 irrigation arms cover?

Track The design of a race track consists of arectangle and two half-circles, as shown in the figure.

a. What is the distance of one lap around the track?

b. A charity walk is 10 kilometers long. How manytimes must participants lap the track to finish the walk?

¢. Suppose a participant is walking at an average speedof 4 kilometers per hour. How long will it take theparticipant to finish the 10-kilometer walk?

I-'ÿ 329 m ÿt

]oo m

6eometryChapter 1 Resource Book 97

Challenge PracticeFor use ÿ4th pages 48-56

I. The, sides of a square are doubled. How does the perimeter and area of thenew square compare with the perimeter and area of the original square?Jtcstify your answer,

2,

3.

The length and width ofa reetangle are doubled, How do the perimeter and areaof the new rectangle compare with the perimeter and area of the original rectangle?Justify your answer,

The figure at the right shows three squares, The area ofsquare I is 25 square inches and the area of square II is64 square inches. What is the perimeter and area ofsquare Ill?

7.

4. The length of a rectangle is 16 centimeters, The perimeter of the rectangle must beat least 36 centimeters and not more than 64 centimeters, Find the interval for thewidth w of the rectangle,

5. The width of a rectangle is 14 meters. The perimeter of the rectangle must be atleast 100 meters and not more than 120 meters, Find the interval for the lengthof the rectangle.

6. The length ÿ of a rectangle is t times its width w, The perimeter of the rectangleis 1200 meters,a. Write the perimeter P of the rectangle in terms ofw and t.

b. Copy and complete the table,

!;!.t:ÿ:(ÿ::ÿ!ÿÿ, 1 1,5 2 3 4 5

c. Describe the relationship among the width, length, and area of a rectangle thathas a fixed perimeter, What dimensions result in a maximum area of the rectangle?

IThe four corners are cut from an 8ÿ--inch-by-I 1-inch piece

of paper as shown in the figure at the right, What is theperimeter of the remaining piece of paper?

-----11 In,--------]-t-.- .

8. Use the figure shown at the right and the PythagoreanTheorem to write a formula for the area.4 of an equilateraltriangle with side x,

,_=

o=

==

}@


Name Date

Cumulative ReviewFor usa a[tÿr Chapter I

Name the object(s) in the diagram. (Lesson 7. 7)

1. Give two other names for AC.

2. Name three points that are collinear.

3. Give another name for plane P.

4. What is another name for CB?

S. Name two pairs of opposite rays.

6. Give another name for EB.

7. Name the intersection of line ÿ and AC.

Plot the given points in a coordinate plane. Then determine whether theline segments named are congruent. (Lessen 1,2)

g. P(5, 2), Q(-3, 2), R(-1, 7), S(-I, -2); PQ andre

9. E(I 5, -9), F(-11, -9), G(-7, 19), H(-7, -7); FE and GH

In each diagram, /V/is the midpoint of the segment. Find the indicatedlength. (Lesson 1.3)

10. Find GM. 11. Find TK

' 2x-3 M x+4 ÿ T 7x-2 ÿ4-4x+ 13

12. Find the coordinates of the midpoint of'the segment with endpoints G(-6, 7) andH(10, - l). (Lesson 1.3)

13. Find the coordinates of the other endpoint of a segment with given endpointQ(2, -3) and midpoint M(-6, -4). (Lesson 1.3)

Use the given information to find the indicated angle measure, (Lesson L4)

14. Given m/ABC = 123°, find mZABD,

(x-o

Given mZJKL = 70°, find mZ MKL,

(x + 31)/.ÿ

K L

)"5

@


e,,PTE, Cumulative Review

Plot the points in a coordinate plane and draw Z TLIV. Classify the angle.Then give the coordinates of a point that lies in the interior of the angle.(Lesson 1,4)

16. T(-l,-2), U(I,4), V(-2,4) 17. T(O, 9), 0(2, 0), V(6,-1)

Z1 and /2 are complementary angles. Given the measure of Z 1, find

mZ2. (Lesson 1.5)

18. mZ! = 35° 19. mZl = 16° 20. rail = 80° 21. mZl = 54°

Tell whether the figure is a polygon and whether it is convexor concave.

23,

g

I24,

Each figure is a regular polygon. Find the value of x. (Lesson 1.ÿ)

25. 26. (x2 + 6x- 20) in. 27.

(2x- 5) em ( ÿ

(X+ 3) cm(xÿ + 2x+ 50} In.

(7X- 2ÿ

(4x+ 16) m

Copy and complete the statement. (Lesson 1,7)

28. 15mÿ=__2__.? cm2 29. 5Oft2=__2_yd2 30. 738 in2 = ?__2__tÿ2

In Exercises 31-33, use the following information, [Lesson 1.7)

Pizza Pan A drcular pizza pan has a diameter of 15 inches,

31, How many inches would be needed to enclose the outside of the pan with acardboard strip?

@ 32. How many square inches of pizza can be made in this pan?.E-• ÿ 33. Would a rectangular pan that measures 12 inches by 15 inches make a larger pizza?

Explain your reasoning.

i;'ÿ,ÿ::{,ÿ

aÿ' ÿ- .ÿ4 ÿ.=-ÿ.ÿ


Name Date

Chapter Test CFor use after Chapter I

In Exercises 1-4, use the diagram.

1. Name the intersection orAL and LO. A L

2, Name the intersection of plane ABC B I .ÿ"ÿ'a,,d plane LO0.

3. Name three planes that intersect at ?.}ÿ-bhÿ-:ÿ'-;ÿ 0

point O. ,.ÿ -ÿ./: :" ":ÿ!ii :" ÿc N4. Name three lines that intersect at

point N.

Answers

1.

2.

3.

4,

5. The midpoint of F'--G is M(- 1, 3). One endpoint is F(-2, 5). Find the

coordinates ofendpoint G.

6. The midpoint of Q-R is M(2, 1.5). One endpoint is R(I, - 1). Find thecoordinates of endpoint Q.

The endpoints of two segments are given. Find the exactlength of each segment. Tell whether the segments are

congruent.

7. x-ÿ;xO, D,B(5,3) s. ÿX; rv0,2),X(5, I)C--D; C(-3, -2), D(-I, 2) -ÿ; }'(4, I), Z(2, 4)

B T

10,

11,

12.

Given that ZABD is a straight ÿ%Cangle, find ,,,LABC and 12x + 9)°ÿ',ÿ10x + 15)°mZ CBD, A B D

Given that ZXYZ and ZLMN arecomplementary angles, findmLXYZ and mZLMN.

Given that / QRS and/EFG are ÿ)0ÿsupplementary angles, findmL QRS and mLEFG, 13x +

O R

X Y

N5x+ 21)°

(7x- 27)0F G:

Given that mL QRT = 95°, findm L QRS and m L SRT.

9,

6.

7,

8,

9°

10.

11,

12,

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a

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Geometry8 Chapter t Assessment 8ook

Chapter Test C1 For use after Chapter /

13. ZFGH and/HGJform a linear pair. Find the measures of theangles ifmZFGH = Ilx° and m/HGJ = (6x - 7)°,

Answers

13.

14. ZLMNand ZNMO form a linear pair, Find tile measures of theangles iI'mZLMN = (3x + 10)° and mZNMO= (2x + 45)°.

Draw a figure that fits the description.

15. A regular triangle 16. A quadrilateral that isequilateral but not equiangular

14.

15.

16.

See left.

See left.

17.

Find the perimeter or circumference of the figure. Use 3.14 forr. Round your answer to the nearest hundredth.

E

,_=

o

@,ÿ,

17. t8.

18.

19.

20.

21.

Find the area of the figure.

19, -- -- ..ÿ "__ 20.

21,-ÿ:-ÿ, .... J

'ÿ I--I- 7T-I- ÿ-- ÿ

. /->- ,.d : -. .'ÿ" .-, ':: .

Jr

Tony walks from point A topoint B and then fi'om point Bto point C as shown in thediagram. How many feet couldhe have saved by walking onthe diagonal sidewalk fi'ompoint A directly to point C?Round your answer to thenearest loot, The distancebetween consecutive gridlines represents 4 feet.

GeometryChapter I Assessment Book 9

Binomials and Factoring Worksheet

Do on own paper.Multiply the following binomials.

1, (x+3)(x+4) 2, (2x+l)(x+4) 3. (6x+ 5)(2x+1)

4. (x-4)(x+4) 5. (x-6)2 6. (6x-5y)2

Factor each of the following polynomials.

1, x2 +8x+15 2. a2-14a+48 3. x2 +x-42

4, x2 - 7x - 18 5. x2 - 16x + 64 6. xu -81

7, 3xZ+16x+5 8. 3a2 +7a+2 9. 2x2 + 5x + 3

10, 8xZ-9x+l 11. 6x2-3X+2 12. lOx2 +17x+3

13. 3xÿ +6xy-24y2 14. 2X3-12xÿy-14xy2 15. 4x2 +100

Solve each quadratic equation using the square root property.

1. x2 =121 2. 3x2 =30 3. 4tz - 25 = 0

4, (x-2)2:49 5. (b-3)2 =6 6, (y+4)z =36

Solve each quadratic equation using factoring.

1. x2 + 7x=O 2. p2-16p+48=O 3. x2+7x+6=O

4. m2+4m=21 5. t2 = 9t-14 6. 2x2 +12x=-lO

unit 1 - pbworks 1... · review 2.1-2.4 test 2.1-2.4 29 30 oct 1 2 3 section 2.5 section 2.6...

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