GSE Geometry Unit 1 & Unit 2 Name: ________________________
Review Date: _______ Pd: ___
_
Use the following figure for question 1.
1. Describe the transformation.
A) translation 6 units down
B) translation 2 units down
C) reflection across the xโaxis
D) reflection across the yโaxis
Use the following figure for question 2.
2. Triangle ABC is reflected across the xโaxis,
and then across the yโaxis. Which rotation
is equivalent to this composition of
transformations?
A) 45 degree rotation
B) 90 degree rotation
C) 180 degree rotation
D) 360 degree rotation
Use the following figure for question 3.
3. If Kite ABCD is reflected across the xโaxis,
what are the resulting coordinates of point
A?
A) (1, โ3)
B) (โ3, 1)
C) (3, โ1)
D) (โ3, โ1)
Find the coordinates of the vertices given the
translation.
4. (x, y) (x + 2, y โ 3)
A(โ4, โ2), B(โ4, โ4), C(โ2, โ4)
A) Aโ(โ6, 1), Bโ (โ6, โ1) Cโ (โ4, โ1)
B) Aโ(โ6, 0), Bโ (6, โ1) Cโ (4, โ1)
C) Aโ(โ2, โ5), Bโ (โ2, โ7), Cโ (0, โ7)
D) Aโ(2, 5), Bโ (2, 7), Cโ (0, 7)
5. (x, y) (x โ 3, y + 1)
A(4, 3), B(1, 3), C(3, 1)
A) Aโ (7, 2) Bโ (4, 2) Cโ (6, 0)
B) Aโ (7, โ2) Bโ (โ4, 2) Cโ (โ6, 0)
C) Aโ (โ1,โ 4) Bโ (2, โ4) Cโ (0, โ2)
D) Aโ (1, 4) Bโ (โ2, 4) Cโ (0, 2)
2
Use the following figure for question 6.
6. Which triangle would be congruent to the
original using a reflection over the xโaxis
and the yโaxis?
A)
B)
C)
D)
Use the following figure for question 7.
7. Which type of transformation is shown
here?
A) dilation
B) reflection
C) rotation
D) translation
Use the following figure for question 8.
8. You are given rectangle ABCD on the grid
shown and are told that the figure is
reflected, but you are not told over which
axis this has occurred. Which COULD be
the new coordinates of point D?
A) (4, โ4)
B) (โ6, โ4)
C) (โ2, โ2)
D) (โ1, โ4)
3
Use the following figure for question 9.
9. The figure is transformed as shown in the
diagram. Describe the transformation.
A) dilation, then reflection
B) reflection, then rotation
C) rotation, then translation
D) translation, then reflection
Find the coordinates of the vertices given the
rotation.
10. 90ยฐ Counterclockwise Rotation about the
Origin
A (3, 2), B (5, 0), C (2, โ3), D (0, โ1)
A) Aโ (2, 3) Bโ (0, 5), Cโ (โ3, 2), Dโ (โ1, 0)
B) Aโ (โ2, โ3) Bโ (0, โ5), Cโ (โ3, โ2), Dโ (โ1, 0)
C) Aโ (โ2, 3) Bโ (0, 5), Cโ (3, 2), Dโ (1, 0)
D) Aโ (3, โ2) Bโ (5, 0), Cโ (2, 3), Dโ (0, 1)
11. 180ยฐ Rotation about the Origin
A (3, 2), B (5, 0), C (2, โ3), D (0, โ1)
A) Aโ (3, 2), Bโ (5, 0), Cโ (2, โ3), Dโ (0, โ1)
B) Aโ (โ3, โ2), Bโ (โ5, 0), Cโ (โ2, โ3), Dโ (0, โ1)
C) Aโ (3, 2), Bโ (5, 0), Cโ (2, 3), Dโ (0, 1)
D) Aโ (โ3, โ2), Bโ (โ5, 0), Cโ (โ2, 3), Dโ (0, 1)
Use the following figure for question 12.
12. The transformation of triangle ABC is an
example of what?
A) Translation of (0, โ8)
B) Translation of (0, 8)
C) A reflection across the yโaxis
D) A reflection across the xโaxis
13. A triangle in the coordinate plane has
coordinates of (2,3), (โ4,โ5), and (โ2, 4). It is
reflected about the yโaxis. What are its new
coordinates?
A) (โ2,3), (4,โ5), (2,4)
B) (โ2,โ3), (4,5), (2,โ4)
C) (2,โ3), (โ4,5), (โ2,โ4)
D) (โ2,โ3), (โ4,โ5), (โ2,โ4)
14. 270ยฐ Counterclockwise Rotation about the
Origin
A(3, 2) B(5, 0) C(2, โ3)D (0, โ1)
A) Aโ (3, 2), Bโ (5, 0), Cโ (2, โ3), Dโ (0, โ1)
B) Aโ (2, โ3), Bโ (0, โ5), Cโ (โ3, โ2),Dโ (โ1, 0)
C) Aโ (โ2, โ3), Bโ (0, โ5),Cโ (โ2, โ2),Dโ (โ1, 0)
D) Aโ (2, โ3), Bโ (0, 5), Cโ (โ3, 2), Dโ (1, 0)
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15. Identify the transformation(s) that will map the image onto itself.
A) Reflect across the xโaxis B) Reflect across the line y = 2 C) Reflect across the line x = 2 D) Reflect across the yโaxis
16. Identify the line of symmetry that the figure is reflected over and label the image.
Use the following figure for question 17.
17. The triangle is transformed as shown in the
diagram. Describe the transformation.
A) dilation, then reflection
B) rotation, then reflection
C) reflection, then rotation
D) translation, then reflection
Use the following figure for question 18.
18. Which transformation will move polygon
ABCD completely into one quadrant?
A) up 5 units
B) left three units
C) reflect over the xโaxis
D) reflect over the yโaxis
Line of Symmetry: _________
A B
C
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19. As shown in the diagram, lines ๐ and ๐ are cut by transversal ๐. If ๐โ 1 = 4๐ฅ + 14 and ๐โ 2 = 8๐ฅ +
10, lines and are parallel when ๐ฅ equals.
A) 1
B) 13
C) 6
D) 17
20. In the diagram, line ๐ intersects lines ๐ and ๐. If ๐โ 1 = 7๐ฅ
and ๐โ 2 = 5๐ฅ + 30, lines ๐ and ๐ are parallel when ๐ฅ equals
A) 12.5
B) 105
C) 87.5
D) 15
21. Lines ๐ and ๐ are intersected by line ๐, as shown. If ๐โ 1 =
7๐ฅ โ 36 and ๐โ 2 = 5๐ฅ + 12 , for which value of x
would ๐ โฅ ๐ ?
A) 97
B) 24
C) 83
D) 17
22. If โ๐ฝ๐พ๐ฟ โ โ๐๐๐, which statement is always true?
A) โ ๐พ๐ฝ๐ฟ โ โ ๐๐๐
B) ๐ฝ๏ฟฝฬ ๏ฟฝ โ ๐๐ฬ ฬ ฬ ฬ ฬ
C) โ ๐พ๐ฟ๐ฝ โ โ ๐๐๐
D) ๐ฝ๐พฬ ฬ ฬ โ ๐๐ฬ ฬ ฬ ฬ
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23. Based on the diagram, which statement is true?
A) ๐ โฅ ๐
B) ๐ โฅ ๐
C) ๐ โฅ ๐
D) ๐ โฅ ๐
24. Give the reason for the last statement in the proof.
Statement Reason
1 and 2 are a linear pair Given
1 and 2 are supplementary ?
A) Congruent Supplements Theorem
B) Congruent Complements Theorem
C) Vertical Angles Congruence Theorem
D) Linear Pair Postulate
25. In the figure shown below, ๐๐ฬ ฬ ฬ ฬ ฬ โ ๐๐ฬ ฬ ฬ ฬ . What is the length of ๐๐ฬ ฬ ฬ ฬ ?
A) 25 B) 34 C) 59 D) 60 E) 84
X W Y Z 3๐ฅ โ 8 2๐ฅ + 3 4๐ฅ + 15
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26. Which of the choices shown could be used to prove that โ๐ด๐ต๐ โ โ๐ถ๐ต๐?
A) SAS
B) HL
C) CPCTC
D) SSA
27. Use the diagram to determine which congruence is correct to prove โ๐๐๐ โ โ๐ฝ๐พ๐ฟ?
A) โ ๐ โ โ ๐พ by SAS Congruence Postulate
B) ๐๐ฬ ฬ ฬ ฬ โ ๐ฝ๐พฬ ฬ ฬ by SAS Congruence Postulate
C) ๐๐ฬ ฬ ฬ ฬ โ ๐ฟ๐พฬ ฬ ฬ ฬ by SAS Congruence Postulate
D) A and B
E) B and C
28. What is the third congruence needed to prove โ๐ด๐ต๐ท โ โ๐ถ๐ต๐ท by AAS?
A) ๐ด๐ตฬ ฬ ฬ ฬ โ ๐ต๐ถฬ ฬ ฬ ฬ
B) โ ๐ท๐ต๐ด โ โ ๐ถ๐ท๐ต
C) ๐ด๐ทฬ ฬ ฬ ฬ โ ๐ท๐ถฬ ฬ ฬ ฬ
D) โ ๐ด๐ต๐ท โ โ ๐ถ๐ต๐ท
E) B or C
29. If โ๐ฝ๐พ๐ฟ โ โ๐๐๐, which statement is always true?
A) โ ๐พ๐ฝ๐ฟ โ โ ๐๐๐
B) โ ๐พ๐ฟ๐ฝ โ โ ๐๐๐
C) ๐ฝ๐พฬ ฬ ฬ โ ๐๐ฬ ฬ ฬ ฬ
D) ๐ฝ๏ฟฝฬ ๏ฟฝ โ ๐๐ฬ ฬ ฬ ฬ ฬ
B
C A P
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30. In the diagram, ๐ด๐ถฬ ฬ ฬ ฬ bisects โ ๐ต๐ด๐ท and โ ๐ต โ โ ๐ท. Which method
could be used to prove โ๐ด๐ต๐ถ โ โ๐ด๐ท๐ถ?
A) AAS B) SSS C) AAA D) SAS
31. Given โ๐ด๐ต๐ท, ๐ต๐ถฬ ฬ ฬ ฬ is the perpendicular bisector of ๐ด๐ทฬ ฬ ฬ ฬ . Which statement Can NOT always be proven?
A) โ๐ด๐ต๐ถ โ โ๐ท๐ต๐ถ
B) ๐ด๐ถฬ ฬ ฬ ฬ โ ๐ท๐ถฬ ฬ ฬ ฬ
C) ๐ต๐ถฬ ฬ ฬ ฬ โ ๐ถ๐ทฬ ฬ ฬ ฬ
D) โ ๐ด๐ถ๐ต โ โ ๐ท๐ถ๐ต
32. Which set of congruence statements shows that โ๐๐๐ถ โ โ๐ ๐บ๐ by the SAS Congruence Theorem in the
reflection below?
A) ๐๐ฬ ฬ ฬ ฬ โ ๐ ๐บฬ ฬ ฬ ฬ ; ๐๐ถฬ ฬ ฬ ฬ โ ๐ ๐ฬ ฬ ฬ ฬ ฬ ; โ ๐๐๐ถ โ โ ๐บ๐ ๐
B) ๐๐ฬ ฬ ฬ ฬ โ ๐ ๐บฬ ฬ ฬ ฬ ; ๐๐ถฬ ฬ ฬ ฬ โ ๐บ๐ฬ ฬ ฬ ฬ ฬ ; โ ๐๐ถ๐ โ โ ๐บ๐๐
C) ๐๐ถฬ ฬ ฬ ฬ โ ๐ ๐ฬ ฬ ฬ ฬ ฬ ; ๐ถ๐ฬ ฬ ฬ ฬ โ ๐๐บฬ ฬ ฬ ฬ ฬ ; โ ๐๐๐ถ โ โ ๐บ๐ ๐
D) ๐๐ถฬ ฬ ฬ ฬ โ ๐ ๐ฬ ฬ ฬ ฬ ฬ ; ๐๐ฬ ฬ ฬ ฬ โ ๐ ๐บฬ ฬ ฬ ฬ ; โ ๐๐ถ๐ โ โ ๐ ๐๐บ
33. In the diagram four pairs of triangles are shown.
Congruent corresponding parts are labeled in each pair.
Using ONLY the information given in the diagrams, which
pair of triangles can NOT be proven congruent?
A) Pair A
B) Pair B
C) Pair C
D) Pair D
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34. In scalene triangle ๐ด๐ต๐ถ, ๐โ ๐ต = 45ยฐ and ๐โ ๐ถ = 55ยฐ. What is the order of the sides in length, from
longest to shortest?
A) ๐ด๐ตฬ ฬ ฬ ฬ , ๐ต๐ถฬ ฬ ฬ ฬ , ๐ด๐ถฬ ฬ ฬ ฬ
B) ๐ต๐ถฬ ฬ ฬ ฬ , ๐ด๐ถฬ ฬ ฬ ฬ , ๐ด๐ตฬ ฬ ฬ ฬ
C) ๐ด๐ถฬ ฬ ฬ ฬ , ๐ต๐ถฬ ฬ ฬ ฬ ฬ , ๐ด๐ตฬ ฬ ฬ ฬ
D) ๐ต๐ถฬ ฬ ฬ ฬ , ๐ด๐ตฬ ฬ ฬ ฬ , ๐ด๐ถฬ ฬ ฬ ฬ
35. In the diagram, ๐๐ด๐๐ป is a rhombus with diagonals ๐ด๐ปฬ ฬ ฬ ฬ and ๐๐ฬ ฬ ฬ ฬ ฬ . If
๐โ ๐ป๐ด๐ = 12ยฐ, what is ๐โ ๐ด๐๐?
A) 12ยฐ
B) 78ยฐ
C) 84ยฐ
D) 156ยฐ
36. In the proof shown here about equilateral triangle โ๐๐๐, what is the correct reason that can be used for
Step 2 and Step 3?
Given: ๐๐ฬ ฬ ฬ ฬ โ ๐๐ฬ ฬ ฬ ฬ โ ๐๐ฬ ฬ ฬ ฬ
Prove: โ ๐ โ โ ๐ โ โ ๐
A) The sum of the interior angles in a triangle is 180ยฐ.
B) If two sides of a triangle are congruent, then the angles opposite the sides are congruent.
C) If two angles of a triangle are congruent, then the sides opposite the angles are congruent.
D) SSS congruence criterion
37. In the diagram, โ๐ฟ๐๐ is isosceles with ๐ฟ๐ = ๐๐. If ๐โ ๐ฟ =
55ยฐ and ๐โ ๐๐๐ = 28ยฐ, what is ๐โ ๐?
A) 27ยฐ
B) 28ยฐ
C) 42ยฐ
D) 70ยฐ
Statements Reasons
1. 1. Given
2. โ ๐ โ โ ๐ 2.
3. โ ๐ โ โ ๐ 3.
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38. Given three distinct quadrilaterals, a square, a rectangle, and a rhombus, which quadrilaterals must
have perpendicular diagonals?
A) The rhombus, only
B) The rectangle and the square
C) The rhombus and the square
D) The rectangle, the rhombus, and the square
39. The lengths of two sides of a triangle are 3 inches and 8 inches. Find the range of possible lengths fo
r the third side, s.
A) 5 < ๐ < 8 B) 3 < ๐ < 11 C) 3 < ๐ < 8 D) 5 < ๐ < 11
40. In the diagram below, ๐ฟ๐ด๐๐ธ is an isosceles trapezoid with ๐ฟ๐ธฬ ฬ ฬ ฬ โ ๐ด๐ฬ ฬ ฬ ฬ , ๐ฟ๐ด = 24, ๐ธ๐ = 40, and ๐ด๐ = 10.
Altitudes ๐ฟ๐นฬ ฬ ฬ ฬ and ๐ด๐บฬ ฬ ฬ ฬ are drawn. What is the length of ๐ฟ๐นฬ ฬ ฬ ฬ ?
A) 6
B) 8
C) 3
D) 4
41. What is the measure of the vertex angle of an isosceles triangle if one of its base
angles measures 42ยฐ?
A) 138ยฐ B) 69ยฐ C) 96ยฐ D) 84ยฐ
42. In the diagram of โ๐ด๐ถ๐, ๐ท is the midpoint of ๐ด๐ถฬ ฬ ฬ ฬ , ๐ is the midpoint of ๐ด๐ฬ ฬ ฬ ฬ , and ๐บ is the midpoint of ๐ถ๐ฬ ฬ ฬ ฬ .
If ๐ด๐ถ = 10, ๐ด๐ = 18, and ๐ถ๐ = 22, what is the perimeter of parallelogram ๐ถ๐ท๐๐บ?
A) 21
B) 25
C) 32
D) 40
๐ช
๐จ
๐ซ
๐ป
๐ถ
๐ฎ
11
18
x
5
12
43. As shown in the diagram of โ๐ด๐ถ๐ท, ๐ต is a point on ๐ด๐ถฬ ฬ ฬ ฬ and ๐ท๐ตฬ ฬ ฬ ฬ is drawn. If ๐โ ๐ด = 66ยฐ, ๐โ ๐ถ๐ท๐ต =
18ยฐ, and ๐โ ๐ถ = 24ยฐ, what it the longest side of โ๐ด๐ต๐ท?
A) ๐ด๐ตฬ ฬ ฬ ฬ
B) ๐ท๐ถฬ ฬ ฬ ฬ
C) ๐ด๐ทฬ ฬ ฬ ฬ
D) ๐ต๐ทฬ ฬ ฬ ฬ
44. In โ๐ท๐ธ๐น, ๐โ ๐ท = (3๐ฅ + 5)ยฐ, ๐โ ๐ธ = (4๐ฅ โ 15)ยฐ, and ๐โ ๐น = (2๐ฅ + 10)ยฐ. Which statement is true?
A) ๐ท๐น = ๐น๐ธ
B) ๐ท๐ธ = ๐น๐ธ
C) ๐โ ๐ธ = ๐โ ๐น
D) ๐โ ๐ท = ๐โ ๐น
45. Two sides of an equilateral triangle have lengths 2๐ฅ โ 2 and 3๐ฅ โ 6 . Which of 10 โ ๐ฅ or 6๐ฅ + 5
could be the length of the third side?
A) neither 10 โ ๐ฅ nor 6๐ฅ + 5
B) 10 โ ๐ฅ only
C) Both 10 โ ๐ฅ and 6๐ฅ + 5
D) 6๐ฅ + 5 only
47. In โ๐ด๐ต๐ถ and โ๐ท๐ธ๐น, ๐ด๐ถ
๐ท๐น=
๐ถ๐ต
๐น๐ธ. Which additional information would prove โ๐ด๐ต๐ถ~โ๐ท๐ธ๐น?
A) โ ๐ต๐ด๐ถ โ โ ๐ธ๐ท๐น B) โ ๐ด๐ถ๐ต โ โ ๐ท๐น๐ธ C) ๐ถ๐ต = ๐น๐ธ D) ๐ด๐ถ = ๐ท๐น
48. Solve for x.
A) ๐ฅ = 25.5 B) ๐ฅ = 11.3 C) ๐ฅ = 3.3 D) ๐ฅ = 7.5
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49. In the figure below, ๐ท๐ธฬ ฬ ฬ ฬ โฅ ๐ด๐ถฬ ฬ ฬ ฬ , ๐ต๐ท = 4, ๐ท๐ด = 6 and ๐ธ๐ถ = 8. Find ๐ต๐ถ to the nearest tenth.
A) 4.3
B) 13.3
C) 5.3
D) 8.2
50. As shown in the diagram, โ๐ด๐ต๐ถ~โ๐ท๐ธ๐น, ๐ด๐ต = 7๐ฅ, ๐ต๐ถ = 4, ๐ท๐ธ = 7, and ๐ธ๐น = ๐ฅ. What is the length
of ๐ด๐ตฬ ฬ ฬ ฬ ?
A) 4
B) 28
C) 2
D) 14
51. When โ๐ด๐ต๐ถ is dilated by a scale factor of 2, its image is โ๐ดโฒ๐ตโฒ๐ถโฒ. Which statement is true?
A) โ ๐ด โ โ ๐ดโ
B) ๐ด๐ถฬ ฬ ฬ ฬ โ ๐ดโฒ๐ถโฒฬ ฬ ฬ ฬ ฬ
C) 2(area of โ๐ด๐ต๐ถ ) = area of โ๐ดโฒ๐ตโฒ๐ถโฒ
D) Perimeter of โ๐ด๐ต๐ถ = perimeter of โ๐ดโฒ๐ตโฒ๐ถโฒ
52. โ๐๐๐ has side lengths 5 cm, 7 cm, and 9 cm. If โ๐๐๐~โ๐ ๐๐, which of the following could be the
lengths of the sides of โ๐ ๐๐ ?
A) 15 cm, 17 cm, and 19 cm
B) 1 cm, 3 cm, 5cm
C) 6 cm, 8.4 cm, and 13.5 cm
D) 7.5 cm, 10.5 cm, 13.5 cm
A C
E
B
D
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53. The triangles formed by two ladders leaning against a wall are
similar. How long is the shorter ladder?
A) 10 ft.
B) 6 ft.
C) 14 ft.
D) 28 ft.
54. In triangles โ๐ด๐ต๐ถ and โ๐ท๐ธ๐น, ๐ด๐ต = 4, ๐ด๐ถ = 5, ๐ท๐ธ = 8, ๐ท๐น = 10, and โ ๐ด โ โ ๐ท. Which method
could be used to prove โ๐ด๐ต๐ถ~โ๐ท๐ธ๐น?
A) ASA B) AA C) SAS D) SSS
55. ๐ด๐ต๐ถ๐ท๐ธ๐น~๐ ๐๐๐๐๐. Find ๐ฅ.
A) 12 in.
B) 2.25 in.
C) 6.75 in.
D) 10 in.
56. If โ๐๐ ๐ is dilated by a scale factor of 1
5 about the origin, which of the following points represents the
coordinates of ๐ โฒ?
A) (โ2
5,
1
5)
B) (โ10, 5)
C) (1
5, โ
2
5)
D) (โ5, 10)
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57. In the figure, โ๐ด๐ต๐ถ~โ๐ดโ๐ตโ๐ถโ. Which statement is true of the
transformation from โ๐ด๐ต๐ถ~โ๐ดโ๐ตโ๐ถโ?
A) The measures of all corresponding angles change by
a scale factor of 1
2.
B) The measures of all corresponding angles change by
a scale factor of 2.
C) The lengths of all corresponding sides change by a
scale factor of 1
2.
D) The lengths of all corresponding sides change by a
scale factor of 2.
58. โ๐ด๐ต๐ถ has vertices ๐ด(1, โ4), ๐ต(โ2, 6) and ๐ถ(5, 2). What are the vertices of the image after a dilation
with a scale factor of 2.5 using the origin as the center of dilation?
A) ๐ดโฒ(2.5, โ10), ๐ตโฒ(โ5, 15), ๐ถโฒ(โ12.5, 5)
B) ๐ดโฒ(โ2.5, 10), ๐ตโฒ(5, โ15), ๐ถโฒ(โ12.5, โ5)
C) ๐ดโฒ(2.5, โ10), ๐ตโฒ(โ5, 15), ๐ถโฒ(12.5, 5)
D) ๐ดโฒ(2.5, โ10), ๐ตโฒ(5, 15), ๐ถโฒ(13, 5)
59. In the diagram, โ๐ด๐ต๐ถ~โ๐ ๐๐. Which statement is NOT true?
A) ๐ด๐ต+๐ต๐ถ+๐ด๐ถ
๐ ๐+๐๐+๐ ๐=
๐ด๐ต
๐ ๐
B) โ ๐ด โ โ ๐
C) ๐ด๐ต
๐ ๐=
๐ต๐ถ
๐๐
D) ๐ด๐ต
๐ต๐ถ=
๐๐
๐ ๐
60. In the triangles shown, โ๐ด๐ต๐ถ is dilated by a factor of 2
3 to form โ๐๐๐.
Given that ๐โ ๐ด = 50ยฐ and ๐โ ๐ต = 100ยฐ, what is ๐โ ๐ยฐ?
A) 30ยฐ
B) 15ยฐ
C) 25ยฐ
D) 50ยฐ