GEOMETRY

PRACTICE

2018-2019

1. Look at the trapezoid shown below.

Which transformation carries the trapezoid onto itself?

A. a reflection across the line y = 0

B. a rotation of 180° about the point(−1,0)

C. a rotation of 180° about the origin

D. a reflection across the line x = –1

2. Two figures are shown below.

Which of the following statements correctly explains whether or not the two figures are congruent?

A. The two figures are not congruent since the two figures are oriented differently.

B. The two figures are congruent since there is a rotation that carries one figure onto the other.

C. The two figures are congruent since there is a reflection that carries one figure onto the other.

D. The two figures are not congruent since there is no translation that carries one figure onto the other.

3. If ΔFGH Δ≅ QRS, find the measure of ∠Q.

A. 9°

B. 11°

C. 28°

D. 34°

4. Which postulate or theorem can be used to prove that ΔABC Δ≅ DCB?

A. SSS

B. SAS

C. ASA

D. AAS

5. Two squares are shown below.

Claudia claims that the two squares are congruent. Which statement could be used to prove Claudia's claim?

A. Any two squares are congruent since all squares have angles of 90°.

B. Any two squares are congruent since all four sides of any square are congruent.

C. The two squares are congruent since a translation carries one square onto the other.

D. The two squares are congruent since a rotation about the origin carries one square onto the other.

6. Which of the following could be the equation of a line parallel to the line y = 4?

A. x = 4

B. y = 0

C. y = 4x

D. undefined

7. On a computer screen, Juana just created a triangular design of a banner with vertices atA(−4,3) ,B(−1,5) , andC (−1,2) . She can use the computer software to perform transformations on this design.Which sequence of two transformations could she perform so that the transformed vertices becomeA' (4 ,−5) , B' (7 ,−7), andC '(7 ,−4) ?

A. translating 6 units down, followed by translating 8 units to the right

B. reflecting about the line y=−2, followed by translating 8 units to the right

C. reflecting about the line y=−1, followed by reflecting about the y -axis

D. reflecting about the liney=−1 , followed by translating 8 units to the right

8. What steps need to be taken so that quadrilateral ABCD can be transformed to overlap quadrilateral A'B'C'D' so that their vertices match?

A. Rotate ABCD 90° clockwise about the origin, then translate it 8 units to the left.

B. Translate ABCD 10 units to the left, then translate it 10 units down.

C. Reflect ABCD about the y-axis, then rotate it 90° counter-clockwise about the origin.

D. Translate ABCD 7 units down, then reflect it about the y-axis.

9. Lucas draws a square and plots the center of the square. He claims that any rotation about the center of the square that is a multiple of 45° will carry the square onto itself.

Which statement best describes Luca’s claim?

A. Luca's claim is correct since any rotation that carries a square onto itself is a multiple of 45°.

B. Luca's claim is correct since any rotation that is a multiple of 45° carries a square onto itself.

C. Luca's claim is incorrect since not all rotations that carry a square onto itself are multiples of 45°.

D. Luca's claim is incorrect since not all rotations that are multiples of 45° carry a square onto itself.

10. On the coordinate plane below, quadrilateral 1 has been transformed to form quadrilateral 2.

Which of these could be the transformation? Choose all that are correct.

A. A reflection across the linex=1

B. A reflection across the liney=1

C. A translation 2 units to the left, and then a reflection across the y -axis

D. A translation 2 units to the right, and then a reflection across the y -axis

E. A reflection across they -axis, and then a translation 2 units to the right

F. A rotation of 180° about the point(1,4)

11. Line MP goes through the points and Which equation represents a line that is perpendicular to FG and passes through the point

A.

B.

C.

D.

12.

In the figure below,

What is the measure of

A. 19.7°

B. 24.4°

C. 79.5°

D. 93.6°

13. Amanda states the following:

"Given two triangles, if two pairs of corresponding sides and one pair of corresponding angles are congruent, then the triangles are congruent by Side–Angle–Side (SAS)."

Which of the following options best describes Amanda's statement?

A. Amanda is correct since SAS requires two pairs of congruent sides and one pair of congruent angles.

B. Amanda is incorrect since SAS is not a congruence criterion that can be used to prove that two triangles are congruent.

C. Amanda is correct since any two pairs of congruent sides and any pair of congruent angles will satisfy the SAS congruence criterion.

D. Amanda is incorrect since triangles with two pairs of congruent sides and one pair of congruent angles do not necessarily meet the SAS criterion.

14. What is the equation of a line perpendicular to  that intersects the line at

A.

B.

C.

D.

15. Two rectangles are shown on the coordinate plane below.

Anthony claims that the two rectangles are congruent. Which of the following statements could he use to prove his claim? Select all that apply.

A. The rectangles are congruent since a translation of 6 units down and 7 units to the left carries Rectangle 1 onto Rectangle 2.

B. The rectangles are congruent since a reflection over the x–axis followed by a translation of 7 units to the right carries Rectangle 1 onto Rectangle 2.

C. The rectangles are congruent since a reflection over the y–axis followed by a translation of 1 unit to the right and 6 units up carries Rectangle 1 onto Rectangle 2.

D. The rectangles are congruent since a rotation of 180° clockwise about the origin followed by a translation of 1 unit to the right carries Rectangle 1 onto Rectangle 2.

E. The rectangles are congruent since a reflection over the x–axis followed by a translation of 5 units to the right carries Rectangle 1 onto Rectangle 2.

16. Sebastian drew oblique segment on a coordinate gird and translated it 4 units to the

left to form  Which statement must be true?

A. lie on the same line.

B. are parallel to each other.

C. are perpendicular to each other.

D. intersect each other, but are not perpendicular.

17.

Which series of transformations can be used to prove that  is congruent to as shown by the graphs below?

 

 

A. rotate 90° counterclockwise about the origin and then translate it 8 units to the right

B. reflect across the line and then translate it 4 units to the left

C. rotate 90° clockwise about the origin and then reflect it across that resulted from the rotation

D. reflect across the line and then reflect it across that resulted from the first reflection

18. Lines l and m are parallel. Line l can be represented by the equation If line m passes through the point which equation can be

used to find the equation of line m?

A.

B.

C.

D.

19. Consider the diagram and angle measurements shown below. 

What is

A.

B.

C.

D.

20.Which of these would prove that triangle PQS is congruent to triangle RQT?

A. Triangle PQS is a dilation of triangle RQT, so the triangles are congruent by AAA.

B. Triangle PQS is a dilation of triangle RQT, so the triangles are congruent by SSS.

C. Triangle PQS is a reflection of triangle RQT, so the triangles are congruent by SSS.

D. Triangle PQS is a reflection of triangle RQT, so the triangles are congruent by AAA.

GeometryAnswer Sheet

Name_______________________________________ Date ________ Period _____

1. _______ 11. ______

2. _______ 12. ______

3. _______ 13. ______

4. _______ 14. ______

5. _______ 15. ______

6. _______ 16. ______

7. _______ 17. ______

8. _______ 18. ______

9. _______ 19. ______

10. _______ 20. ______