Name __________________________ Date ___________________ Teacher________________ Group_____________
GEOMETRY
Figure One
1. In Figure One the letter ”Z” has been rotated 180° about
Point P to produce the image as a dotted line. Which answer
choice shows this particular transformation?
a. A
b. B
c. C
d. D
2. Which of the following transformations does not produce
a congruent image?
a. Translation
b. Dilation
c. Reflection
d. Rotation
3. Which of the coordinates listed below produce a rectangle that is a translation of the rectangle shown
in Figure Two ?
a. { (0, 3), (0, 9), (5, 3), (5, 9) }
b. { (0, 0), (0, 3), (5, 0), (5, 3) }
c. { (0, 0), (4, 0), (0, 4) }
d. { (7, 0), (7, 3), (12, 0), (12, 3)
Figure Two
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4. From the statements made below, which is the only true statement?
a. All right triangles are congruent.
b. All squares are congruent.
c. If two isosceles triangles have the same base length, they are congruent.
d. If two squares have sides of the same length, they are congruent.
5. What are the coordinates of ΔA’B’C’ after ΔABC
has been reflected across the x-axis ?
a. A’⇒ (2, −1)
B’⇒ (4, −2)
C’⇒ (3, −4)
b. A’⇒ (−2,1)
B’⇒ (−4,2)
C’⇒ (−3,4)
c. A’⇒ (−1,2)
B’⇒ (−2,4)
C’⇒ (−4,3)
d. A’⇒ (2, −1)
B’⇒ (3, −4)
C’⇒ (4, −2)
6. Which coordinates form a triangle that is a translation of the triangle shown below?
a. (−1,5), (5,5), (2,12)
b. (1,1), (10,1), (16,5)
c. (−1,1), (5,1), (2,8)
d. (2,0), (2,3), (15,0)
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7. Which two transformations have occurred in the coordinate plane in Figure Three for ΔDEF to form
ΔD’E’F’ ?
a. a rotation of 180° clockwise and a reflection across the xaxis
b. a rotation of 90° counterclockwise and a translation by
using the rule (𝑥, 𝑦) → (𝑥 − 2, 𝑦 )
c. a reflection across the x-axis and a rotation of 180°
clockwise
d. a translation by using the rule (𝑥, 𝑦) → (𝑥 + 3 − 2, 𝑦 + 10 )
and a reflection across the x-axis
Figure Three
8. The coordinate plane shown to the right has
Figure H in the fourth quadrant and its image,
Figure H', in the second quadrant. Which of the
following series of transformations would result
in the image shown?
a. reflecting Figure H across the y-axis and then
translating it up
b. rotating Figure H 180° and then reflecting it across
the x-axis
c. translating Figure H up and then translating it left
d. reflecting Figure H across the y-axis and then
reflecting it across the x-axis
9. Which of the following terms is used in geometry and refers to two or more figures, when
superimposed, retain the same size and same shape.
a. dilation
b. corresponding
c. congruent
d. slope
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10. In the graph below, which of the following translation rules accurately describes the transformation
from ΔABC to ΔA’B’C’ ?
a. (𝑥 – 4, 𝑦 – 3)
c. (𝑥 + 4, 𝑦 − 3)
b. (𝑥 − 4, 𝑦 + 3)
d. (𝑥 + 4, 𝑦 + 3)
11. A triangle is defined on the coordinate plane with vertices at (0, 0), (3, 1), and (4, 5). Which two
transformations would result in a triangle similar to the original?
a. if the triangle was dilated by a factor of 2 centered on the origin
b. the triangle is translated 2 units along the y-axis, then reflected over the x-axis
c. the triangle is reflected over the x-axis, rotated 90°, and then dilated by a factor of 2
d. if the measure of the angle formed by the two shorter sides is increased or decreased, such that the
opposing side of the triangle becomes the longest side of the newly formed triangle.
12. Which sequence of transformations on ΔRST would
produce the same image as that of 180° rotation?
a. a translation of 9 units to the left
and 10 units down
b. a rotation of 270° counterclockwise
and then a reflection across the y-axis
c. reflecting ΔRST across the x-axis and
then reflecting it across the y-axis
d. translating ΔRST 10 units down and
then reflecting it across the y-axis
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Use the triangle in Figure Four to answer questions 13-15
13. Which set of coordinates would be
the coordinates of the given triangle after
it has been dilated by a scale factor of
1
with the center of dilation at the origin?
2
a. (1,2), (2,4), (3,2)
b. (−2, −4), (−4, −8), (−6, −4)
c. (4,8), (8,16), (12,8)
d. (1,4), (2,8), (3,4)
Figure Four
14. After dilating ΔABC in Question 13,
what is the exact length of ̅̅̅̅̅̅
𝐴′𝐵′ ?
̅̅̅̅̅̅ rounded to
15. What is the length of 𝐴′𝐵′
the nearest tenth of a unit?
a. √3 units
b. √5 units
a. 2.5 units
b. 5.2 units
c. 3 units
d. 5 units
c. 2.0 units
d. 2.2 units
Use Figure Five to answer Questions 16 and 17
Figure Five
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16. Figure Five shows the squares of the lengths of three sides that form a right triangle. Assuming the
area of Square Q is 32 units 2 and Square R has an area of 48 units2 , what is the area of Square S?
units2
17. What is the length of the side of Square S in units, rounded to the nearest tenth?
units
18. What is the length (in units) of segment AB
shown in the coordinate plane to the right,
rounded to the nearest tenth?
a. 7.1 units
b. 8.9 units
c. 8.1 units
d. 7.9 units
B
A
19. Which of the following are the sides of a right triangle?
a. 2 inches, 8 inches, 10 inches
b. 5 feet, 11 feet, 13 feet
c. 8 miles, 8 miles, 10 miles
d. 8 cm, 15 cm, 17 cm
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⃡ intersecting them to create Angles A-H. Use Figure Six to answer
⃡∥⃡
In Figure Six assume 𝒑
𝒒 with 𝒌
questions 20-23.
Figure Six
q
p
A
C
B
D
F
H
G
E
k
20. Which of the following statements is false?
a. ∠B is congruent to ∠H becuause they are alternate exterior angles and alternate exterior angles are
congruent.
b. If 𝑚∠D = 32°, then 𝑚∠C = 158°.
c. Since ∠A and ∠G are supplementary angles, ∠A + ∠G = 180°.
⃡ is not parallel to ⃡
d. If 𝒑
𝒒, then ∠E ≇ ∠A.
21. From the following angle pairs listed below, choose every pair that are corresponding angles.
a. ∠D and ∠G
b. ∠A and ∠F
c. ∠C and ∠H
f. ∠E and ∠D
g. ∠A and ∠B
h. ∠C and ∠G
d. ∠F and ∠E
e. ∠G and ∠H
22. By assuming the measure of ∠B = 122°,
what could we then assume is the measure
of ∠H ?
23. What is the alternate interior angle
pair for ∠D?
a. 122°
b. 58°
a. ∠G
b. ∠E
c. 180°
d. 158°
c. ∠C
d. ∠F
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24. In the figure shown below Line j intersects Line k to form Angles A, B, C, and D. There are two pairs
of vertical angles and there are four pairs of adjacent angles.
j
D
A
C
B
k
PART ONE: Fill in the missing sections of the table listing each vertical and adjacent angle.
Adjacent Angles
Vertical Angles
∠A and ∠B
∠A and ∠C
PART TWO: Draw a picture below using only two intersecting lines, in which the adjacent angles would
be congruent.
PART THREE: What is the measure of the adjacent angles?
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25. The ruins of The Parthenon in Athens, Greece is one of the most popular tourist destinations in all of
Europe. Built in 447 BC during the Athenian Empire as a temple, The Parthenon’s structure can still be
seen today. The outer perimeter of the temple (seen below) is lined with columns, common to Greek
architecture during that time. Of the over thirty columns that surround the temple, most are up to 6 feet
in diameter and 34 feet tall. The mixture needed to make the columns was a limestone/marble mined
from a quarry over 20 miles away so the volume of each column was calculated before construction. The
Greco-Roman architecture of The Parthenon and its world renowned columns have stood the test of time
with thousands of visitors touring the ancient temple each year.
With each column having a radius of around three feet and a height of 34 feet, what is the approximate
volume in cubic feet of each one of The Parthenon’s famous columns?
a. 961.3 ft 3
b. 640.9 ft 3
b. 320.4 ft 3
d. 2,142.2 ft 3
26. What is the radius of a basketball if the maximum volume the ball can hold is 904.8 in3 ?
a. 4 inches
b. 5 inches
c. 6 inches
d. 7 inches
27. An ice cream cone has a diameter of 6cm and a height of 20cm. What is the volume of the ice cream
cone?
a. 565.5 cm3
b. 188.5 cm3
c. 2261.9 cm3
d. 753.9 cm3
Name __________________________ Date ___________________ Teacher________________ Group_____________
28. Find the value of x to determine which answer choice provides the correct angle measures in Figure
Seven.
Figure Seven
a. 𝑚∠𝐷𝐶𝐵 = 50°
𝑚∠𝐶𝐵𝐷 = 70°
b. 𝑚∠𝐷𝐶𝐵 = 45°
𝑚∠𝐶𝐵𝐷 = 75°
c. 𝑚∠𝐷𝐶𝐵 = 33°
𝑚∠𝐶𝐵𝐷 = 87°
d. 𝑚∠𝐷𝐶𝐵 = 60°
𝑚∠𝐷𝐶𝐵 = 60°
29. Determine the coordinates of B’ C’ Z’ X’ if it is rotated 90° counterclockwise about the origin.
The original quadrilateral is displayed below in the coordinate plane.
Z B’ ____________
X
C
B’ ______________
C’ ______________
Z’ ______________
B
X’ ______________
30. A 55” television is on sale at Walmart for $498. The way
televisions are measured is diagonally from one corner to the
other (see picture). If the height of the television is 35”,
approximately how long would the television be in inches
rounded to the nearest tenth?
a. 65 inches
b. 90 inches
c. 55 inches
d. 42 inches
55’’
35’’
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