gse geometry unit 1 & unit 2 name: review date:...

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 x–axis

D) reflection across the y–axis


2. Triangle ABC is reflected across the x–axis,

and then across the y–axis. 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


3. If Kite ABCD is reflected across the x–axis,

what are the resulting coordinates of point

A?

A) (1, –3)

B) (–3, 1)

C) (3, –1)

D) (–3, –1)

Find the coordinates of the vertices given the

translation.

4. (x, y) (x + 2, y – 3)

A(–4, –2), B(–4, –4), C(–2, –4)

A) A’(–6, 1), B’ (–6, –1) C’ (–4, –1)

B) A’(–6, 0), B’ (6, –1) C’ (4, –1)

C) A’(–2, –5), B’ (–2, –7), C’ (0, –7)

D) A’(2, 5), B’ (2, 7), C’ (0, 7)

5. (x, y) (x – 3, y + 1)

A(4, 3), B(1, 3), C(3, 1)

A) A’ (7, 2) B’ (4, 2) C’ (6, 0)

B) A’ (7, –2) B’ (–4, 2) C’ (–6, 0)

C) A’ (–1,– 4) B’ (2, –4) C’ (0, –2)

D) A’ (1, 4) B’ (–2, 4) C’ (0, 2)

2


6. Which triangle would be congruent to the

original using a reflection over the x–axis

and the y–axis?

A)

B)

C)

D)


7. Which type of transformation is shown

here?

A) dilation

B) reflection

C) rotation

D) translation


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, –4)

B) (–6, –4)

C) (–2, –2)

D) (–1, –4)

3


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. 90° Counterclockwise Rotation about the

Origin

A (3, 2), B (5, 0), C (2, –3), D (0, –1)

A) A’ (2, 3) B’ (0, 5), C’ (–3, 2), D’ (–1, 0)

B) A’ (–2, –3) B’ (0, –5), C’ (–3, –2), D’ (–1, 0)

C) A’ (–2, 3) B’ (0, 5), C’ (3, 2), D’ (1, 0)

D) A’ (3, –2) B’ (5, 0), C’ (2, 3), D’ (0, 1)

11. 180° Rotation about the Origin

A (3, 2), B (5, 0), C (2, –3), D (0, –1)

A) A’ (3, 2), B’ (5, 0), C’ (2, –3), D’ (0, –1)

B) A’ (–3, –2), B’ (–5, 0), C’ (–2, –3), D’ (0, –1)

C) A’ (3, 2), B’ (5, 0), C’ (2, 3), D’ (0, 1)

D) A’ (–3, –2), B’ (–5, 0), C’ (–2, 3), D’ (0, 1)


12. The transformation of triangle ABC is an

example of what?

A) Translation of (0, –8)

B) Translation of (0, 8)

C) A reflection across the y–axis

D) A reflection across the x–axis

13. A triangle in the coordinate plane has

coordinates of (2,3), (–4,–5), and (–2, 4). It is

reflected about the y–axis. What are its new

coordinates?

A) (–2,3), (4,–5), (2,4)

B) (–2,–3), (4,5), (2,–4)

C) (2,–3), (–4,5), (–2,–4)

D) (–2,–3), (–4,–5), (–2,–4)

14. 270° Counterclockwise Rotation about the

Origin

A(3, 2) B(5, 0) C(2, –3)D (0, –1)

A) A’ (3, 2), B’ (5, 0), C’ (2, –3), D’ (0, –1)

B) A’ (2, –3), B’ (0, –5), C’ (–3, –2),D’ (–1, 0)

C) A’ (–2, –3), B’ (0, –5),C’ (–2, –2),D’ (–1, 0)

D) A’ (2, –3), B’ (0, 5), C’ (–3, 2), D’ (1, 0)

4

15. Identify the transformation(s) that will map the image onto itself.

A) Reflect across the x–axis B) Reflect across the line y = 2 C) Reflect across the line x = 2 D) Reflect across the y–axis

16. Identify the line of symmetry that the figure is reflected over and label the image.


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


18. Which transformation will move polygon

ABCD completely into one quadrant?

A) up 5 units

B) left three units

C) reflect over the x–axis

D) reflect over the y–axis

Line of Symmetry: _________

A B

C

5

19. As shown in the diagram, lines 𝑚 and 𝑛 are cut by transversal 𝑝. If 𝑚∠1 = 4𝑥 + 14 and 𝑚∠2 = 8𝑥 +

10, lines and are parallel when 𝑥 equals.

A) 1

B) 13

C) 6

D) 17

20. In the diagram, line 𝑝 intersects lines 𝑚 and 𝑛. If 𝑚∠1 = 7𝑥

and 𝑚∠2 = 5𝑥 + 30, lines 𝑚 and 𝑛 are parallel when 𝑥 equals

A) 12.5

B) 105

C) 87.5

D) 15

21. Lines 𝑝 and 𝑞 are intersected by line 𝑟, as shown. If 𝑚∠1 =

7𝑥 − 36 and 𝑚∠2 = 5𝑥 + 12 , for which value of x

would 𝑝 ∥ 𝑞 ?

A) 97

B) 24

C) 83

D) 17

22. If ∆𝐽𝐾𝐿 ≅ ∆𝑀𝑁𝑂, which statement is always true?

A) ∠𝐾𝐽𝐿 ≅ ∠𝑀𝑂𝑁

B) 𝐽�̅� ≅ 𝑀𝑂̅̅ ̅̅ ̅

C) ∠𝐾𝐿𝐽 ≅ ∠𝑁𝑀𝑂

D) 𝐽𝐾̅̅ ̅ ≅ 𝑂𝑁̅̅ ̅̅

6

23. Based on the diagram, which statement is true?

A) 𝑎 ∥ 𝑏

B) 𝑎 ∥ 𝑐

C) 𝑑 ∥ 𝑒

D) 𝑏 ∥ 𝑐

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, 𝑊𝑋̅̅ ̅̅ ̅ ≅ 𝑌𝑍̅̅̅̅ . What is the length of 𝑋𝑍̅̅ ̅̅ ?

A) 25 B) 34 C) 59 D) 60 E) 84

X W Y Z 3𝑥 − 8 2𝑥 + 3 4𝑥 + 15

7

26. Which of the choices shown could be used to prove that ∆𝐴𝐵𝑃 ≅ ∆𝐶𝐵𝑃?

A) SAS

B) HL

C) CPCTC

D) SSA

27. Use the diagram to determine which congruence is correct to prove ∆𝑋𝑌𝑍 ≅ ∆𝐽𝐾𝐿?

A) ∠𝑌 ≅ ∠𝐾 by SAS Congruence Postulate

B) 𝑋𝑌̅̅ ̅̅ ≅ 𝐽𝐾̅̅ ̅ by SAS Congruence Postulate

C) 𝑍𝑌̅̅̅̅ ≅ 𝐿𝐾̅̅ ̅̅ by SAS Congruence Postulate

D) A and B

E) B and C

28. What is the third congruence needed to prove ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷 by AAS?

A) 𝐴𝐵̅̅ ̅̅ ≅ 𝐵𝐶̅̅ ̅̅

B) ∠𝐷𝐵𝐴 ≅ ∠𝐶𝐷𝐵

C) 𝐴𝐷̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅

D) ∠𝐴𝐵𝐷 ≅ ∠𝐶𝐵𝐷

E) B or C

29. If ∆𝐽𝐾𝐿 ≅ ∆𝑀𝑁𝑂, which statement is always true?

A) ∠𝐾𝐽𝐿 ≅ ∠𝑀𝑂𝑁

B) ∠𝐾𝐿𝐽 ≅ ∠𝑁𝑀𝑂

C) 𝐽𝐾̅̅ ̅ ≅ 𝑂𝑁̅̅ ̅̅

D) 𝐽�̅� ≅ 𝑀𝑂̅̅ ̅̅ ̅

B

C A P

8

30. In the diagram, 𝐴𝐶̅̅ ̅̅ bisects ∠𝐵𝐴𝐷 and ∠𝐵 ≅ ∠𝐷. Which method

could be used to prove ∆𝐴𝐵𝐶 ≅ ∆𝐴𝐷𝐶?

A) AAS B) SSS C) AAA D) SAS

31. Given ∆𝐴𝐵𝐷, 𝐵𝐶̅̅ ̅̅ is the perpendicular bisector of 𝐴𝐷̅̅ ̅̅ . Which statement Can NOT always be proven?

A) ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐵𝐶

B) 𝐴𝐶̅̅ ̅̅ ≅ 𝐷𝐶̅̅ ̅̅

C) 𝐵𝐶̅̅ ̅̅ ≅ 𝐶𝐷̅̅ ̅̅

D) ∠𝐴𝐶𝐵 ≅ ∠𝐷𝐶𝐵

32. Which set of congruence statements shows that ∆𝑃𝑆𝐶 ≅ ∆𝑅𝐺𝑀 by the SAS Congruence Theorem in the

reflection below?

A) 𝑃𝑆̅̅̅̅ ≅ 𝑅𝐺̅̅ ̅̅ ; 𝑃𝐶̅̅ ̅̅ ≅ 𝑅𝑀̅̅̅̅̅ ; ∠𝑆𝑃𝐶 ≅ ∠𝐺𝑅𝑀

B) 𝑃𝑆̅̅̅̅ ≅ 𝑅𝐺̅̅ ̅̅ ; 𝑆𝐶̅̅̅̅ ≅ 𝐺𝑀̅̅̅̅̅ ; ∠𝑆𝐶𝑃 ≅ ∠𝐺𝑀𝑅

C) 𝑃𝐶̅̅̅̅ ≅ 𝑅𝑀̅̅̅̅̅ ; 𝐶𝑆̅̅̅̅ ≅ 𝑀𝐺̅̅ ̅̅̅ ; ∠𝑆𝑃𝐶 ≅ ∠𝐺𝑅𝑀

D) 𝑃𝐶̅̅̅̅ ≅ 𝑅𝑀̅̅̅̅̅ ; 𝑃𝑆̅̅̅̅ ≅ 𝑅𝐺̅̅ ̅̅ ; ∠𝑃𝐶𝑆 ≅ ∠𝑅𝑀𝐺

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

9

34. In scalene triangle 𝐴𝐵𝐶, 𝑚∠𝐵 = 45° and 𝑚∠𝐶 = 55°. What is the order of the sides in length, from

longest to shortest?

A) 𝐴𝐵̅̅ ̅̅ , 𝐵𝐶̅̅ ̅̅ , 𝐴𝐶̅̅ ̅̅

B) 𝐵𝐶̅̅ ̅̅ , 𝐴𝐶̅̅ ̅̅ , 𝐴𝐵̅̅ ̅̅

C) 𝐴𝐶̅̅ ̅̅ , 𝐵𝐶̅̅ ̅̅̅, 𝐴𝐵̅̅ ̅̅

D) 𝐵𝐶̅̅ ̅̅ , 𝐴𝐵̅̅ ̅̅ , 𝐴𝐶̅̅ ̅̅

35. In the diagram, 𝑀𝐴𝑇𝐻 is a rhombus with diagonals 𝐴𝐻̅̅ ̅̅ and 𝑀𝑇̅̅̅̅̅. If

𝑚∠𝐻𝐴𝑀 = 12°, what is 𝑚∠𝐴𝑀𝑇?

A) 12°

B) 78°

C) 84°

D) 156°

36. In the proof shown here about equilateral triangle ∆𝑋𝑌𝑍, what is the correct reason that can be used for

Step 2 and Step 3?

Given: 𝑋𝑌̅̅ ̅̅ ≅ 𝑌𝑍̅̅̅̅ ≅ 𝑋𝑍̅̅ ̅̅

Prove: ∠𝑋 ≅ ∠𝑌 ≅ ∠𝑍

A) The sum of the interior angles in a triangle is 180°.

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, ∆𝐿𝑀𝑂 is isosceles with 𝐿𝑂 = 𝑀𝑂. If 𝑚∠𝐿 =

55° and 𝑚∠𝑁𝑂𝑀 = 28°, what is 𝑚∠𝑁?

A) 27°

B) 28°

C) 42°

D) 70°

Statements Reasons

1. 1. Given

2. ∠𝑋 ≅ ∠𝑌 2.

3. ∠𝑌 ≅ ∠𝑍 3.

10

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 < 𝑠 < 8 B) 3 < 𝑠 < 11 C) 3 < 𝑠 < 8 D) 5 < 𝑠 < 11

40. In the diagram below, 𝐿𝐴𝑇𝐸 is an isosceles trapezoid with 𝐿𝐸̅̅̅̅ ≅ 𝐴𝑇̅̅ ̅̅ , 𝐿𝐴 = 24, 𝐸𝑇 = 40, and 𝐴𝑇 = 10.

Altitudes 𝐿𝐹̅̅̅̅ and 𝐴𝐺̅̅ ̅̅ are drawn. What is the length of 𝐿𝐹̅̅̅̅ ?

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 42°?

A) 138° B) 69° C) 96° D) 84°

42. In the diagram of ∆𝐴𝐶𝑇, 𝐷 is the midpoint of 𝐴𝐶̅̅ ̅̅ , 𝑂 is the midpoint of 𝐴𝑇̅̅ ̅̅ , and 𝐺 is the midpoint of 𝐶𝑇̅̅̅̅ .

If 𝐴𝐶 = 10, 𝐴𝑇 = 18, and 𝐶𝑇 = 22, what is the perimeter of parallelogram 𝐶𝐷𝑂𝐺?

A) 21

B) 25

C) 32

D) 40

𝑪

𝑨

𝑫

𝑻

𝑶

𝑮

11

18

x

5

12

43. As shown in the diagram of ∆𝐴𝐶𝐷, 𝐵 is a point on 𝐴𝐶̅̅ ̅̅ and 𝐷𝐵̅̅ ̅̅ is drawn. If 𝑚∠𝐴 = 66°, 𝑚∠𝐶𝐷𝐵 =

18°, and 𝑚∠𝐶 = 24°, what it the longest side of ∆𝐴𝐵𝐷?

A) 𝐴𝐵̅̅ ̅̅

B) 𝐷𝐶̅̅ ̅̅

C) 𝐴𝐷̅̅ ̅̅

D) 𝐵𝐷̅̅ ̅̅

44. In ∆𝐷𝐸𝐹, 𝑀∠𝐷 = (3𝑥 + 5)°, 𝑚∠𝐸 = (4𝑥 − 15)°, and 𝑚∠𝐹 = (2𝑥 + 10)°. Which statement is true?

A) 𝐷𝐹 = 𝐹𝐸

B) 𝐷𝐸 = 𝐹𝐸

C) 𝑚∠𝐸 = 𝑚∠𝐹

D) 𝑚∠𝐷 = 𝑚∠𝐹

45. Two sides of an equilateral triangle have lengths 2𝑥 − 2 and 3𝑥 − 6 . Which of 10 − 𝑥 or 6𝑥 + 5

could be the length of the third side?

A) neither 10 − 𝑥 nor 6𝑥 + 5

B) 10 − 𝑥 only

C) Both 10 − 𝑥 and 6𝑥 + 5

D) 6𝑥 + 5 only

47. In ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, 𝐴𝐶

𝐷𝐹=

𝐶𝐵

𝐹𝐸. Which additional information would prove ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹?

A) ∠𝐵𝐴𝐶 ≅ ∠𝐸𝐷𝐹 B) ∠𝐴𝐶𝐵 ≅ ∠𝐷𝐹𝐸 C) 𝐶𝐵 = 𝐹𝐸 D) 𝐴𝐶 = 𝐷𝐹

48. Solve for x.

A) 𝑥 = 25.5 B) 𝑥 = 11.3 C) 𝑥 = 3.3 D) 𝑥 = 7.5

12

49. In the figure below, 𝐷𝐸̅̅ ̅̅ ∥ 𝐴𝐶̅̅ ̅̅ , 𝐵𝐷 = 4, 𝐷𝐴 = 6 and 𝐸𝐶 = 8. Find 𝐵𝐶 to the nearest tenth.

A) 4.3

B) 13.3

C) 5.3

D) 8.2

50. As shown in the diagram, ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹, 𝐴𝐵 = 7𝑥, 𝐵𝐶 = 4, 𝐷𝐸 = 7, and 𝐸𝐹 = 𝑥. What is the length

of 𝐴𝐵̅̅ ̅̅ ?

A) 4

B) 28

C) 2

D) 14

51. When ∆𝐴𝐵𝐶 is dilated by a scale factor of 2, its image is ∆𝐴′𝐵′𝐶′. Which statement is true?

A) ∠𝐴 ≅ ∠𝐴’

B) 𝐴𝐶̅̅ ̅̅ ≅ 𝐴′𝐶′̅̅ ̅̅ ̅

C) 2(area of ∆𝐴𝐵𝐶 ) = area of ∆𝐴′𝐵′𝐶′

D) Perimeter of ∆𝐴𝐵𝐶 = perimeter of ∆𝐴′𝐵′𝐶′

52. ∆𝑁𝑂𝑃 has side lengths 5 cm, 7 cm, and 9 cm. If ∆𝑁𝑂𝑃~∆𝑅𝑆𝑇, which of the following could be the

lengths of the sides of ∆𝑅𝑆𝑇 ?

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

13

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 ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹, 𝐴𝐵 = 4, 𝐴𝐶 = 5, 𝐷𝐸 = 8, 𝐷𝐹 = 10, and ∠𝐴 ≅ ∠𝐷. Which method

could be used to prove ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹?

A) ASA B) AA C) SAS D) SSS

55. 𝐴𝐵𝐶𝐷𝐸𝐹~𝑅𝑆𝑇𝑈𝑉𝑄. Find 𝑥.

A) 12 in.

B) 2.25 in.

C) 6.75 in.

D) 10 in.

56. If ∆𝑄𝑅𝑆 is dilated by a scale factor of 1

5 about the origin, which of the following points represents the

coordinates of 𝑅′?

A) (−2

5,

1

5)

B) (−10, 5)

C) (1

5, −

2

5)

D) (−5, 10)

14

57. In the figure, ∆𝐴𝐵𝐶~∆𝐴’𝐵’𝐶’. Which statement is true of the

transformation from ∆𝐴𝐵𝐶~∆𝐴’𝐵’𝐶’?

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. ∆𝐴𝐵𝐶 has vertices 𝐴(1, −4), 𝐵(−2, 6) and 𝐶(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) 𝐴′(2.5, −10), 𝐵′(−5, 15), 𝐶′(−12.5, 5)

B) 𝐴′(−2.5, 10), 𝐵′(5, −15), 𝐶′(−12.5, −5)

C) 𝐴′(2.5, −10), 𝐵′(−5, 15), 𝐶′(12.5, 5)

D) 𝐴′(2.5, −10), 𝐵′(5, 15), 𝐶′(13, 5)

59. In the diagram, ∆𝐴𝐵𝐶~∆𝑅𝑆𝑇. Which statement is NOT true?

A) 𝐴𝐵+𝐵𝐶+𝐴𝐶

𝑅𝑆+𝑆𝑇+𝑅𝑇=

𝐴𝐵

𝑅𝑆

B) ∠𝐴 ≅ ∠𝑅

C) 𝐴𝐵

𝑅𝑆=

𝐵𝐶

𝑆𝑇

D) 𝐴𝐵

𝐵𝐶=

𝑆𝑇

𝑅𝑆

60. In the triangles shown, ∆𝐴𝐵𝐶 is dilated by a factor of 2

3 to form ∆𝑋𝑌𝑍.

Given that 𝑚∠𝐴 = 50° and 𝑚∠𝐵 = 100°, what is 𝑚∠𝑍°?

A) 30°

B) 15°

C) 25°

D) 50°

gse geometry unit 1 & unit 2 name: review date:...

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