STAAR GEOMETRY REVIEW Reporting Category 4
1
(G.8) Congruence and the geometry of size:
The student uses tools to determine measurements of
geometric figures and extends measurement concepts to find perimeter, area, and volume in
problem situations.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.8)(A) - Find areas of regular polygons, circle, and composite figures. (READINESS STANDARD)
Academic Language Notes
Area
Regular Polygon
Circle
Composite Figure
STAAR GEOMETRY REVIEW Reporting Category 4
2
(G.8)(A) Find areas of regular polygons, circle, and composite figures. (READINESS STANDARD)
1. A pizza has a diameter of 16 inches. Which is closest to the area of one slice if the pizza is divided
into 6 equal pieces?
A. 134.1 sq in.
B. 117.1 sq in.
C. 67.2 sq in.
D. 33.5 sq in.
2.
The lengths of two consecutive sides of the
parallelogram shown are 10 inches and 15
inches. The two sides include an angle of 60o.
To the nearest tenth of a square inch,
what is the area of the parallelogram?
F. 21.6 in.2
G. 129.9 in. 2
_
H. 139.4 in. 2
J. 140.5 in. 2
3.
What is the area of the unshaded part of the
rectangle to the right?
A. 19,000 ft2
B. 45,000 ft2
C. 28,000 ft2
D. 26,000 ft2
STAAR GEOMETRY REVIEW Reporting Category 4
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4. The figure on the right shows a CD in its
rectangular storage case. Which is closest to
the area of the storage case not occupied by
the CD?
F. 55 cm2
G. 46 cm2
H. 51 cm2
J. 60 cm2
5.
The dimensions of 3 connected stores are
shown to the right. How many square feet of
floor space are used by the 3 stores?
A. 9,600 ft 2
B. 11,280 ft 2
C. 21,141 ft 2
D. 42,021 ft 2
6.
What is the total area of the polygon shown?
F. 126 ft2
G. 450 ft2
H. 600 ft2
J. 900 ft2
STAAR GEOMETRY REVIEW Reporting Category 4
4
7. The area rug pictured below is 6
feet wide by 9 feet long. If each
side of each white hexagon
measures 1.8 ft, then what is the
total area of the gray portions of
this rug?
A. 13.5 ft2
B. 11.91 ft2
C. 40.5 ft2
D. 54 ft2
8.
Below is the top view of a hexagonal gazebo which is built on a round cement foundation that has
an area of 8m2. The roof is made up six equilateral triangles with beams that extend 0.25m
beyond the roof on all six vertices. To the nearest tenth, approximately how much of the cement
foundation is not covered by the roof?
F. 3.3 m2
G. 4.7 m2
H. 6.6 m2
J. 9.5 m2
9.
A custom cover is ordered to fit the swimming pool shown below. One end of the pool has a
whirlpool sitting area in the shape of a semi-circle with the rest in the shape of a rectangle. What
is the approximate total area that the pool cover must have?
A. 480 ft2
B. 540 ft2
C. 560 ft2
D. 620 ft2
STAAR GEOMETRY REVIEW Reporting Category 4
5
(G.8) Congruence and the geometry of size:
The student uses tools to determine measurements of
geometric figures and extends measurement concepts to find perimeter, area, and volume in
problem situations.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.8)(B) Find areas of sectors and arc lengths of circles using proportional reasoning. (Supporting Standard)
Academic Language Notes
Sector
Central Angle
Arc
Measure of an Arc
Arc Length
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.8)(B) Find areas of sectors and arc lengths of circles using proportional reasoning. (Supporting Standard)
1.
Jeanette is embroidering the border of a
Christmas tree skirt. Her design only
covers the gray regions. To the nearest
tenth of a square foot, how much area will
be covered with Jeanette’s embroidery
work, if the radius of the tree skirt is 2.5 ft
and the width of the square is 3.5 ft?
A. 5.0 ft2
B. 7.4 ft2
C. 12.3 ft2
D. 19.6 ft2
2.
This circle, with center point Q, has a radius
of 10 centimeters. The length of the minor arc
NP is 20.42 centimeters. To the nearest
degree, what is the value of x?
F. 110º
G. 117º
H. 204º
J. 233º
STAAR GEOMETRY REVIEW Reporting Category 4
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3. A granite piece is being fashioned to fit over a fireplace. A segment must be cut out to fit over the
arch of the fireplace opening. What is the approximate area of the finished granite arch?
(Use 3.14 for and round your answer to the nearest whole number.)
A. 873 in2 B. 1071 in
2 C. 1264 in
2 D. 1944 in
2
4.
If Jeff ran one-third of the way around a track with a 50-meter radius, approximately how far did
he run?
F. 15 m G. 50 m H. 105 m J. 246 m
STAAR GEOMETRY REVIEW Reporting Category 4
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5. A rotary lawn sprinkler can be adjusted to water any part of a whole circle. The sprinkler is
located at the corner of a cement patio so that it can water the surrounding area of grass as shown.
If the sprinkler can spray at a maximum distance of 20 feet, how much watering coverage does the
sprinkler provide?
A. 314 ft2 B. 1256 ft
2 C. 942 ft
2 D. 3768 ft
2
6.
The measure of a given arc within a circle
with a radius of 4 inches is 50o. Determine
the length of the arc to the nearest hundredth
of an inch.
Record your answer and fill in the bubbles
on grid.
STAAR GEOMETRY REVIEW Reporting Category 4
9
(G.8) Congruence and the geometry of size:
The student uses tools to determine measurements of
geometric figures and extends measurement concepts to find perimeter, area, and volume in
problem situations.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.8)(C) - Extend, and use the Pythagorean Theorem. (READINESS STANDARD)
Academic Language Notes
Right Triangle
Hypotenuse
Pythagorean Theorem
STAAR GEOMETRY REVIEW Reporting Category 4
10
(G.8)(C) Extend, and use the Pythagorean Theorem. (READINESS STANDARD)
1.
Kim walked diagonally across a
rectangular field that measured 100 feet by
240 feet. Which expression could be used
to determine how far Kim walked?
A. 2 (100 + 240)
B. 100 + 240
C. 2
240*100
D. 22 )240()100(
3. ∆WXY is isosceles. WY is 10 centimeters
long. Find the length of XZ.
A. 5 cm
B. 10 cm
C. 12 cm
D. 13 cm
2. About how many feet of fencing are
needed to enclose a rectangular garden
with a 30-foot-long side and a 40-foot-
long diagonal?
F. 113 ft
G. 133 ft
H. 140 ft
J. 160 ft
4.
Trapezoid LKNP is shown below.
Which is closest to the area of trapezoid
LKNP?
F. 276 in. 2
G. 205 in. 2
H. 289 in. 2
J. 221 in. 2
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5. The figure below is constructed of
isosceles right triangles. Given that
and = 2 in., then what is the
area of the entire shape? Round your
answer to the nearest tenth.
A. 9.9 in2
B. 13.9 in2
C. 15.1 in2
D. 30.2 in2
6.
The figure below is constructed of similar
right triangles. Given that AO = 4 inches
and AB = 3 inches, then what is the
approximate area of the entire shape?
Round your answer to the nearest tenth.
A. 36.0 in2
B. 53.1 in2
C. 106.1 in2
D. 115.1 in2
7.
Computer "Screen Size" is measured from
the lower left corner to the upper right
corner of the screen. If the diagonal of the
screen is 15 inches and the width of the
screen is 12 inches, then what is the height
of the computer screen?
A. 8 inches
B. 9 inches
C. 10 inches
D. 11 inches
STAAR GEOMETRY REVIEW Reporting Category 4
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8. The total area of trapezoid FGHJ is 52
square inches. What is the approximate
length of segment FJ?
A. 8.0 inches
B. 8.5 inches
C. 11.0 inches
D. 11.5 inches
9.
A couple of friends are out flying a kite. When they get it off the ground, the “flyer” lets out 300 ft
of string. Meanwhile, the “launcher” is 120 ft away from his friend and directly under the kite. To
the nearest tenth, what is the altitude of the kite?
F. 20.5 ft2
G. 180 ft2
H. 275 ft2
J. 323.1 ft2
G F
JH
5 inches
8 inches
8 inches
STAAR GEOMETRY REVIEW Reporting Category 4
13
(G.8) Congruence and the geometry of size:
The student uses tools to determine measurements of
geometric figures and extends measurement concepts to find perimeter, area, and volume in
problem situations.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: G.8)(D) - Find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations. (READINESS STANDARD)
Academic Language Notes
Lateral Area
Lateral Face
Surface Area
Volume
Cubic Unit
Composite Figures
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.8)(D) Find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations. (READINESS STANDARD)
1. Miguel has a cylinder with the dimensions
shown below. The cylinder is filled to
capacity with water.
If Miguel wants to pour all the water in
this cylinder into 1 of the 4 rectangular
prisms below without any water spilling
out of the prism, which of the following
prisms should he use?
STAAR GEOMETRY REVIEW Reporting Category 4
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2. Henry built a wooden storage shed in the
shape of a rectangular prism for his tools.
The figure on the right shows the
dimensions of the storage shed. If Henry
plans to paint only the top, front, left, and
right sides of his shed, which is closest to
the surface area that will be painted?
F. 121 ft2
G. 181 ft2
H. 154 ft2
J. 91ft2
3.
Oatmeal is packaged in a cylindrical
container with the dimensions shown in
the drawing. Find the approximate volume
of this oatmeal container.
A. 471 cubic centimeters
B. 566 cubic centimeters
C. 1413 cubic centimeters
D. 5655 cubic centimeters
4.
A jewelry box has the dimensions shown
on the right. What is the volume of this
figure to the nearest tenth?
F. 24 in2
G. 61.7 in2
H. 37.7 in2
J. 99.4 in2
10 centimeters
18 centimeters
OATMEAL
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5.
A box is tightly packed with three cylinders. The dimensions of the box are shown. What is the
volume of the box that is not occupied by the cylinders?
A. 1290.6 in3 B. 1570.8 in
3 C. 4712.8 in
3 D. 5700.0 in
3
6.
In cold climates, buildings are often designed to reduce heat loss by minimizing the exposed
surface area. Determine the approximate surface area of the building that has the least amount of
heat loss.
F. Building A:
628 m2
G. Building B:
628 m2
H. Building A:
704 m2
J. Building B:
704 m2
STAAR GEOMETRY REVIEW Reporting Category 4
17
(G.8) Congruence and the geometry of size:
The student uses tools to determine measurements of
geometric figures and extends measurement concepts to find perimeter, area, and volume in
problem situations.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.8)(E) Use area models to connect geometry to probability and statistics. (Supporting Standard)
Academic Language Notes
Area Model
Probability
Experimental Probability
Theoretical Probability
Percent
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.8)(E) Use area models to connect geometry to probability and statistics. (Supporting Standard)
1. Juana rolls two 6-sided number cubes labeled 1 through 6. Which area model can Juana use to
correctly determine the probability that one of the number cubes will have a 3 facing up and the
other will have an even number facing up?
2.
Geraldo has a rectangular plot of land, as shown at
the right, with the dimensions of 17 feet by 22 feet.
If he plans to use the shaded portion as a garden and
build a gazebo with a diameter of 12 feet,
approximately what percentage of the land will be
used as a garden?
F. 30%
G. 70%
H. 21%
J. 79%
A. B.
C. D.
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3. The following table represents the results of an experiment.
Number of People Choosing the Color
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Red Red Red Red Red Red Red Red Red Red
Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
What is the experimental probability of a person choosing yellow?
A. 37.5% B. 12.5% C. 25% D. 20%
4.
The shaded region of this map shows the dimensions of a state park. What percentage of the map is
not a state park?
F. 27% G. 73% H. 54% J. 89%
5.
A point is randomly selected on XY . What is the probability that it will be closer to the midpoint of
XY than to either endpoints, X or Y?
A. 4
1 B.
3
1 C.
2
1 D.
4
3
STAAR GEOMETRY REVIEW Reporting Category 4
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6. The figure below shows a game board.
A top is spun on the game board and points are awarded based on where the top finally stops. The
edges of the board are raised so that the top will stay on the game board. If the top is equally likely
to stop anywhere on the board, what is the probability that it will stop in a shaded region?
F. 143
2% G 18
3
2% H. 24% J. 29
3
1%
7.
To win a carnival game, Katherine must
throw a dart at a board that is 4 feet by 3 feet
and hit one of the 25 circles on the board.
The diameter of each circle is 4 inches.
Approximately what percent of the time will
a randomly thrown dart that hits the board
also hit a circle? Round your answer to the
nearest tenth of a percent.
Record your answer and fill in the
bubbles on grid.
STAAR GEOMETRY REVIEW Reporting Category 4
21
(G.8) Congruence and the geometry of size:
The student uses tools to determine measurements of
geometric figures and extends measurement concepts to find perimeter, area, and volume in
problem situations.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: G.8)(F) - Use conversions between measurement systems to solve problems in real-world situations. (Supporting Standard)
Academic Language Notes
Customary system
Metric system
Unit conversion
Proportion
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.8)(F) Use conversions between measurement systems to solve problems in real-world situations. (Supporting Standard)
1. The world’s fastest flying insect is the
dragonfly. It can fly 36 miles per hour. If a
dragonfly flew in a straight path at this rate,
what distance would it fly in 15 minutes?
A. 2 miles
B. 9 miles
C. 25 miles
D. 540 miles
3. A patient is to take 1.2 grams of Tylenol
every 8 hours. The prescription he obtains is
in milligrams. Accordingly, said patient
should take how many milligrams of Tylenol
every 8 hours?
F. 1200 mg
G. 12 mg
H. 1.2 mg
J. 120 mg
2. James runs the 100 meter-dash in 11.50
seconds. Accordingly, James is running
approximately how many feet per second?
F. 28.52 ft
G. 8.7 ft
H. 31.2 ft
J. 13.62 ft
4. If the Indy 500 was looking to revamp its
racing name from “500” miles to kilometers,
what would the new name look like?
A. Indy 250
B. Indy 625
C. Indy 805
D. Indy 1000
5.
The dimensions of the box are 18 inches,
2 feet and 1 yard. What is the volume of
the box in cubic feet? Record your
answer and fill in the bubbles on grid.
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.9) Congruence and the geometry of size: The student analyzes
properties and describes relationships in geometric figures.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.9)(A) - Formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models. (Supporting Standard)
Academic Language Notes
Parallel lines
Perpendicular lines
Transversal
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles
Same-Side Interior Angles
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.9)(A) Formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models. (Supporting Standard)
For #1 – 2, use the diagram below in which
line m line n and line l is a transversal that
passes through lines m and n.
For #3 – 4, use the diagram below in which
line p line r and are both cut by two
transversals.
1. Which of the following pairs of angles are
not supplementary?
A. 1 and 2
B. 1 and 6
C. 1 and 5
D. 1 and 7
3. The angles pairs 1 and 2, 2 and 4,
4 and 3, 3 and 1 all represent what
relationship?
A. same side interior angles
B. same side exterior angles
C. complementary angles
D. supplementary angles
2. If m 3 = 2x + 7 and the m 6 = 45o,
determine the value of x.
F. 15
G. 26
H. 19
J. 64
4. If m 3 = 57o and the m 9 = 115
o,
determine m 7.
F. 57o
G. 58 o
H. 115 o
J. 60 o
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5. Selena is using strings to mark parallel rows
for a vegetable garden behind her house.
If m 1 is 115o, what should be m 2?
A. 25o
B. 65o
C. 75o
D. 115o
7. Transversal l cuts lines a, b, c and d.
Which two lines are parallel?
A. a and c
B. a and d
C. b and c
D. b and d
6. On PQ , R is between P and Q. Point X
does not line on PQ and XR is not
perpendicular to PQ . Which of the
following describes XRQ and XRP?
F. complementary angles
G. congruent angles
H. supplementary angles
J. vertical angles
8. The support legs on a bench are attached in
such a way that the angle make by one leg
with the ground is 130o.
What must the measure of the angle marked
x be in order for the seat of the bench to be
parallel to the ground?
F. 50o
G. 65 o
H. 90 o
J. 130 o
STAAR GEOMETRY REVIEW Reporting Category 4
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9. A carpenter nailed a board across two
beams, forming the angles shown.
Which equal measures would ensure that the
beams are parallel?
A. m 1 = m 2
B. m 1 = m 3
C. m 2 = m 5
D. m 3 = m 4
10. Line p is a transversal.
For lines q, r, s, and t, which is not parallel to
the other three lines?
A. q
B. r
C. s
D. t
11.
Two triangles are joined such that AD and
BC are both perpendicular to AB and CD
is perpendicular to AC . If mBCA = 35o
what is mCDA?
Record your answer and fill in the
bubbles on grid.
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.9) Congruence and the geometry of size: The student analyzes
properties and describes relationships in geometric figures.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.9)(B) Formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models. (Supporting Standard)
Academic Language Notes
Regular Polygon
Side of a Polygon
Vertex of a Polygon
Diagonal
Concave
Convex
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.9)(B) Formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models. (Supporting Standard)
1.
A supporting beam for a porch forms two
angles with a vertical beam in the outside
wall where the porch is attached to the
house. What is the measure of the larger
angle formed by the support and the
vertical beam?
A. 25
B. 50
C. 65
D. 155
3.
Find the values of x and y in circle A.
A. x = 20, y = 25
B. x = 40, y = 50
C. x = 40, y = 100
D. x = 80, y = 100
2. In polygon ABCD, mA = 49°,
mB = 107°, and m C = 2 m D.
What is mC?
F. 24o
G. 102o
H. 68o
J. 136o
4. Which statement is true?
F. Every rhombus is a square.
G. Every parallelogram is a rectangle.
H. Every square is a rectangle.
J. Every quadrilateral is a trapezoid.
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5. Jared was trying to build a ramp for his
little brother and was going to make it in
the shape of an isosceles triangle. He was
trying to decide what all of the angle
measures should be. One angle measure
of his isosceles triangle was 84°. Give
two possible pairs of measures for the
other two angles.
A. 12° and 12°; 48° and 96°
B. 48° and 84°; 12° and 48°
C. 84° and 12°; 48° and 48°
D. 96° and 12°; 84° and 48°
7. Circle K and circle L are congruent circles
that intersect at M and N. MN is the common
chord of the circles.
What kind of quadrilateral is KMLN?
A. rectangle
B. rhombus
C. square
D. trapezoid
6. The sum of the measures of the interior
angles of a polygon is five times the sum
of the measures of its exterior angles, one
angle at each vertex. How many sides
does the polygon have?
F. 6
G. 12
H. 18
J. 24
8. Which statement is not true about a regular
16-gon?
F. It is a convex polygon.
G. It has 16 congruent sides.
H. The sum of the interior angle measures
2880°.
J. The sum of the exterior angles, one at each
vertex, is 360°.
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9. Two sides of a triangle have lengths 45
inches and 50 inches. How long can the
third side be?
A. between 5 inches and 50 inches
B. between 5 inches and 95 inches
C. between 45 inches and 50 inches
D. between 5 inches and 45 inches
11. Jaime was trying to cut a piece of wood into a
triangular shape that he could draw on for his
art class. Which of the following sets of
numbers could be lengths of three sides of his
wood project?
A. 4, 5, 8
B. 7, 12, 23
C. 10, 11, 30
D. 14, 18, 37
10. In quadrilateral ABCD, mA = x,
mB = 2x, mC = 3x, and mD = 4x.
Find the value of x and then state which pair
of sides of ABCD must be parallel.
F. x = 3; AD and BD
G. x = 10; CD and DA
H. x = 18; AB and BC
J. x = 36; AB and CD
12. While doing a research project on bees and
beehives, Caitlyn noticed that the face of a
honeycomb consists of interlocking regular
hexagons. What is the measure of each
interior angle of these hexagons?
F. 60°
G. 90°
H. 100°
J. 120°
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.9) Congruence and the geometry of size: The student analyzes
properties and describes relationships in geometric figures.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.9)(C) Formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models. (Supporting Standard)
Academic Language Notes
Chord
Secant
Tangent of a Circle
Point of Tangency
Central Angle
Arc
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(G.9)(C) Formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models. (Supporting Standard)
For # 1 – 2, use the diagram of circle O
shown below.
3. In the figure below, mMLP = 35o.
What is mMOP?
A. 35o
B. 70o
C. 125o
D. 145o
1. Which of the following best describes RS
in relation to the circle O?
A. radius
B. diameter
C. secant
D. tangent
2. Which of the following best describes XY
in relation to the circle O?
F. chord
G. diameter
H. secant
J. tangent
4. P has center P (3,-2) and radius 2. Which
of these lines is tangent to P?
F. x = 0
G. y = -4
H. y = -2
J. x = 4
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5.
An airplane pilot is flying across the equator.
He can see along an arc of the equator that
stretches from C to D. What is the measure of
arc CD? (Note that the figure is not drawn
to scale.)
A. 3°
B. 4°
C. 5°
D. 6°
6.
A new playground has a sand-filled play area
for small children. The company that built
the play area made the measurements of the
play area shown in the figure. If the play area
is circular, what should the value of x be?
F. 4 yd
G. 4.5 yd
H. 5 yd
J. 5.5 yd
7.
AP is tangent to circle O at A, circle O has
a radius of 6 ft and circle P has a radius of 2 ft.
If AB = 6 ft, what is CD?
Record your answer and fill in the
bubbles on grid.
STAAR GEOMETRY REVIEW Reporting Category 4
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For 8 – 9, use the figure below in which PA
is tangent to the circle C at point A and the
diameter of the circle is 4 centimeters.
For 10 -11, use the figure below in which
KH is tangent to circle F at point K and
circle G at point J. GJ = 6; JH = 8; FH = 30.
8. What is PF? Round to the nearest
hundredth of a centimeter.
A. 7.25 cm
B. 7.39 cm
C. 8.40 cm
D. 10 cm
10. What is FK?
A. 16
B. 18
C. 20
D. 24
9. What is DE? Round to the nearest
hundredth of a centimeter.
F. 1.75 cm
G. 2.25 cm
H. 2.75 cm
J. 3.75 cm
11. What is KJ?
F. 16
G. 18
H. 20
J. 24
STAAR GEOMETRY REVIEW Reporting Category 4
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(G.9) Congruence and the geometry of size: The student analyzes
properties and describes relationships in geometric figures.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.9)(D) Analyze the characteristics of polyhedral and other three-dimensional figures and their component parts based on explorations and concrete models. (Supporting Standard)
Academic Language Notes
Polyhedron
Cone
Cylinder
Net
Prism
Pyramid
Sphere
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(G.9)(D) Analyze the characteristics of polyhedral and other three-dimensional figures and their component parts based on explorations and concrete models. (Supporting Standard)
1. Which of the following regular solids has 4
vertices, 4 faces, and 6 edges?
A. Cube
B. Tetrahedron
C. Octahedron
D. Icosahedron
3. How many faces, edges, and vertices does a
hexagonal pyramid have?
A. {6,10,6}
B. {7,12,7}
C. {7,10,7}
D. {8,18,12}
2. How many faces, edges, and vertices does
a regular dodecahedron have?
F. {12, 30, 20}
G. {20, 30, 12}
H. {6, 12, 8}
J. {8, 12, 6}
4. For the polyhedron pictured here, describe
how many faces, edges, and vertices it has.
F. {20, 12, 10}
G. {10, 12, 10}
H. {10, 20, 12}
J. {12, 20, 10}
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(G.10) Congruence and the geometry of size:
The student applies the concept of congruence to
justify properties of figures and solve problems.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.10)(A) Use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane. (Supporting Standard)
Academic Language Notes
Translation
Reflection
Rotation
Congruent Polygons
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(G.10)(A) Use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane. (Supporting Standard)
1. Jerome performs a translation on a
polygon graphed on the coordinate plane
by using . Derek
performs another translation on the same
polygon using .
What single translation could have been
performed on the object so that the same
result would have been achieved?
A.
B.
C.
D.
2. has as its vertices P(8, 2), Q(-2, 2),
R(0, 6), S(-6, 6). It is rotated about the
origin in a clockwise direction. Which of the
following points cannot be one of the
resulting vertices?
F. (2, -2)
G. (6, 6)
H. (2, 8)
J. (6, 0)
3.
For any image reflected over the x-axis, which of the following statements must always be true in
order to maintain congruence?
A. The image keeps the original y-coordinate and the opposite of the x-coordinate.
B. The image keeps the original x-coordinate and the opposite of the y-coordinate.
C. The x-coordinate becomes the y-coordinate and vice versa.
D. The x- and y-coordinates both become their opposites.
4.
For any image reflected over the y-axis, which of the following statements must always be true in
order to maintain congruence?
F. The image keeps the original y-coordinate and the opposite of the x-coordinate.
G. The image keeps the original x-coordinate and the opposite of the y-coordinate.
H. The x-coordinate becomes the y-coordinate and vice versa.
J. The x- and y-coordinates both become their opposites.
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5.
∆KQT is graphed on the grid. Which of the following best represents an image of ∆KQT
translated 2 units to the left and reflected across the x-axis?
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6. Parallelogram WBMP is shown on the grid below.
If WBMP is reflected across the line y = −x and then translated 4 units down to become
parallelogram W’B’M’P’ , what will be the coordinates of M’ ?
F. (−6, −7)
G. (6, −1)
H. (6, 7)
J. (6, 3)
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(G.10) Congruence and the geometry of size:
The student applies the concept of congruence to
justify properties of figures and solve problems.
Name: ____________________________________________________
Date: ____________________________________________________
Period: ____________________________________________________
Topic: (G.10)(B) - Justify and apply triangle congruence relationships. (READINESS STANDARD)
Academic Language Notes
Corresponding Angles
Corresponding Sides
Congruent Polygons
Triangle Rigidity
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(G.10)(B) Justify and apply triangle congruence relationships (READINESS STANDARD)
1. Find the values of x and y.
A. x = 90, y = 47
B. x = 43, y = 47
C. x = 47, y = 43
D. x = 90, y = 43
3. Which theorem or postulate can be used to
prove that ∆CAN is congruent to ∆BNA?
A. SSS
B. ASA
C. AAS
D. SAS
2. Name the theorem or postulate that
lets you conclude
F. SAS
G. ASA
H. AAS
J. none of these
4. If two sides and the included angle of one
triangle are congruent to the two sides and
the included angle of another triangle, then
the triangles are congruent. What theorem or
postulate is being applied?
F. Side-Angle-Side
G. Angle-Side-Angle
H. Side-Side-Side
J. Angle-Angle-Side
ABD CBD.
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5.
To prove the two triangles congruent by
using the Angle-Side-Angle
Congruence Postulate, what other piece of
information is needed?
A C E
B C D
C A D
D A E
7.
What theorem or postulate could be used to
prove that ∆ABC is congruent to ∆DBC?
A Side Angle Side
B Angle Side Angle
C Side Side Side
D Angle Angle Side
6.
Which theorem or postulate can be used to
prove that ∆ABC is congruent to ∆EDC?
F SAS
G AAS
H ASA
J SSS
8. Which of the following does not refer to a
theorem or postulate used to
prove triangles congruent?
F SAS
G SSA
H ASA
J SSS
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9. In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by
ASA?
A.
C.
B.
D.
10.
What additional information is needed to
prove ∆MNL congruent to ∆PNO by SAS?
F MN PN
G LM OP
H M P
J L O
11.
What additional information is needed to
prove that ∆MNL is congruent to ∆PNO by
ASA?
A MN PN
B LM OP
C M P
D L O