Geometry

Final Exam Review

Mr. Belanger

Problem #1Ch.8 Right Triangles

What is the Pythagorean Theorem?

Apply it to this problem..

222 138 q

64 + 169

Q= 15.3

233

Problem #2Ch. 8 Right Triangles

What are the three trigonometry ratios we learned???

SIN =

COS=

TAN=

Hypotenuse

Opposite

Adjacent

hypotenuse

opposite

hypotenuse

adjacent

adjacent

opposite

Problem #3Ch. 8 Right Triangles

1030sin

x X=5

1030cos

y Y=8.7

x

8

6)( xTan

xTan

8

61

X=36.9

c

12.531sin

31sin

12.5c

C=9.9

Problem #4Ch. 9 Transformations

Another name?

Translation or slide

Beginning/End Shapes

Pre-image/image

Properties??

Congruent angles and sides

Problem #5Ch. 9 Transformations

Mirror LineProperties???

A

A’

Shapes are congruent

Orientation is reversed

Points are equidistant from mirror line

B

B’ Cross at 90 degrees

ReflectionReflection

Problem #6Ch. 9 Transformations

Rotation

Rotation and Reflection

Reflection

Rotation and point

Name the type(s) of symmetry for each…

Problem #7Transformations

What is a dilation?

Size change with shapes reduction/enlargement

Properties?

•Angles don’t change•Sides are proportional•Shapes are similar•New coordinates found by multiplying

Problem #8Ch. 10 Area

• Parallelogram/Rectangle/Square

• Triangle

• Trapezoid

• Kite/Rhombus

Know the area formulas for…

Base X HeightBase X Height

2

hb

2

21 bbh

221 dd

Problem #9Ch. 10 Area

•Circle (area) (circumference)

•Polygon

•SAS Triangle Area

2

sinsideside

2

perimeterapothem

2r d

Problem #10Ch. 10 Area

Find the Area of each shape below…

25.172

75cm

2302

106un

Problem #11Ch. 10 Area

Find the Area of each shape below…

225.212

65.25cm

12 cm

22 4.45212 cm

Problem #12Ch. 11 Surface Area and Volume

a

b c

d

e

f g

h

Name one of each…

Vertex-

Edge-

Lateral Face-

Base-

a

ab

dcgh

abcd

Name the shape- Rectangular prism

Problem #13Ch. 11 Surface Area and Volume

What is lateral area???

Area of all lateral sides (walls) added together

What is surface area???

Area of all faces added together

What is volume???

How much space is inside an object

Problem #14Ch. 11 Surface Area and Volume

Find the LA, SA and Volume of prism below.

LA = FBLR

20

203030

LA =100 cm squared

SA = LA + 2 basesSA = LA + 2 basesSA = 100 + 24 + 24 = 148 cm squared

Volume = Area of base x height.Volume = Area of base x height.

Vol = 4 x 6 x 5 = 120 cm cubed

Problem #15Ch. 11 Surface Area and Volume

Find the LA, SA and Volume of prism below.

10 in

3 inLA = Label of can (circumference x height)

22 rrLASA 21.2453.283.285.188 inSA

Volume = area of base x height

32 7.282103 inVol

2 5.188106 inLA

Problem #16Ch. 11 Surface Area and Volume

Find the LA, SA and Volume of pyramid below.

5 in

5 in

12

13 slant height

LA = area of four triangles added LA = area of four triangles added togethertogether

213042

513inLA

SA = LA + one baseSA = LA + one base

SA = 130 + 25 = 155 in sq.

3

height) base of ( areaVol

Vol = 100 in cubed

Problem #17Ch. 12 Circle Properties

If line YK is tangent to the circle, find its length.

222 2410 x576100 2 x

4762 x

X= 21.8

Problem #18Ch. 12 Circle Properties

56

Omfind

90 + 90 + 56 + O = 360

124Om

Problem #19Ch. 12 Circle Properties

-Chords are segments!

-Diameter is a chord that passes through center

-Secant is a line!

-Tangent is a line that touches the circle at one point perpendicular to the radius.

Tangent

Problem #20Ch. 12 Circle Properties

78 APBmfind

Angles are half the size of their intercepted arc

APB = 39

Problem #21Ch. 12 Circle Properties

Know all your secant properties…

angle

2

21.1 inside

arcarc

angleoutside

arcarc

2

21.2

1 2

12

Problem #22Ch. 12 Circle Properties

dcba .3 a

b

c

d

Inside segment

4. Outside segment

5. Secant-tangent

Problem #23Ch. 12 Circle Properties

8

2

7

x

x 728x716 x3.2

Study your old tests and quizzes!Study your old tests and quizzes!Ch. 8-12Ch. 8-12