Transformations, Congruence, Similarity

Multiple Choice

1. Figure RST has been rotated 90o clockwise to form figure OPQ.

Which of the following statements is true?

• A. 𝑚∠𝑅 ≅𝑚∠𝑄

• B. 𝑚∠𝑆≅𝑚∠𝑃

• C. 𝑅𝑆 ≅ 𝑃𝑄

• D. 𝑆𝑇 ≅ 𝑂𝑃

Multiple Choice

2. Trapezoid ABCD has been translated down and to the right to form trapezoid RSTU.

Given that 𝐴𝐵 ∥ 𝐷𝐶, which of the following statements is true?

• A. 𝐴𝐵 ≅ 𝐷𝐶

• B. 𝑆T ≅ 𝑈𝑇

• C. 𝐴𝐵 ∥ 𝑅𝑆

• D. 𝑅𝑆 ∥ 𝑈𝑇

Multiple Choice

3. Figure ABCD has been reflected across the y-axis to form figure WXYZ. Which of the following statements is true?

• A. 𝑚∠𝐴 ≅𝑚∠𝑌

• B. 𝑚∠𝐷≅𝑚∠𝑋

• C. 𝐴𝐵 ≅ 𝑊𝑋

• D. 𝐴𝐵 ≅ 𝑌𝑍

Multiple Choice

4. Rectangle ABCD has been rotated $$90\degree$$ clockwise and reflected across the x-axis to form rectangle A’B’C’D’.

What is true about the rectangles?

• A. Rectangle ABCD is congruent to rectangle A’B’C’D’.

• B. Rectangle ABCD is similar but not congruent to rectangle A’B’C’D’.

• C. Rectangle ABCD has the same angle measures as A’B’C’D’ but different side lengths.

• D. Rectangle ABCD has no relationship with Rectangle A’B’C’D’.

Multiple Choice

5. Which sequence of transformations might have happened in order for figure QRSTU to form Q’R’S’T’U’ as shown to the left?

• A. Reflection across the x-axis, translation 3 units left.

• B. Reflection across the x-axis, translation 3 units right.

• C. Reflection across the y-axis, translation 4 units up.

• D. Reflection across the y-axis, translation 4 units down.

Multiple Choice

6. Which sequence of transformations could triangle XYZ have gone through to produce figure X’Y’Z’ as shown to the left?

• A. Rotation $$90\degree$$ clockwise, translation 4 units up and 3 units right.

• B. Rotation $$90\degree$$ counterclockwise, translation 3 units up and 4 units right.

• C. Rotation $$90\degree$$ clockwise, reflection across the y-axis

• D. Rotation $$90\degree$$ counterclockwise, reflection across the y-axis.

Multiple Choice

7. Line segment RS is shown below with coordinates R (-8, -3) and S (3, -3). Which coordinate below would represent R’ if point R was reflected across the x-axis?

• A. (-8, 3)

• B. (3, 3)

• C. (8, -3)

• D. (-3, -3)

Multiple Choice

8. If parallelogram ABCD is translated left two units and down 5 units, what is the resulting

coordinate of B’ ?

• A. (10, 2)

• B. (8, 2)

• C. (6, 7)

• D. (6, 2)

Multiple Choice

9. If figure EFGHI is rotated $$270\degree$$ counter-clockwise about the origin, What would be the resulting coordinate of point F’?

• A. (-3, -5)

• B. (-5, -3)

• C. (5, 3)

• D. (5, -3)

Multiple Choice

10. If trapezoid QRST is dilated about the origin by a scale factor (k) of 2, what is the resulting coordinate of point T’?

• A. (6, 2)

• B. (-5, -4)

• C. (-6, -4)

• D. (-1, -4)

Multiple Choice

11. Rectangle ABCD has been translated 5 units down and dilated by a scale factor (k) of ½ to form rectangle A’B’C’D’. What is true about the rectangles?

• A. Rectangle ABCD is congruent to rectangle A’B’C’D’.

• B. Rectangle ABCD is similar but not congruent to rectangle A’B’C’D’.

• C. Rectangle ABCD has the same side lengths but different angle measures than rectangle A’B’C’D’.

• D. Rectangle ABCD has no relationship with Rectangle A’B’C’D’.

Multiple Choice

12. Which sequence of transformations might have happened in order for figure QRSTU to form Q’R’S’T’U’ as shown to the left?

• A. Rotation $$90\degree$$ clockwise, dilation using k = 3/2

• B. Rotation $$180\degree$$ , dilation using k = 1/3

• C. Rotation $$90\degree$$ clockwise, dilation using k = 1/3

• D. Rotation $$180\degree$$ , dilation using k = 3/2

Multiple Choice

13. Which sequence of transformations could triangle XYZ have gone through to produce figure X’Y’Z’ as shown to the left?

• A. Reflection across the y-axis, dilation using k = 2

• B. Reflection across the y-axis, dilation using k = ½

• C. Reflection across the x-axis, dilation using k = 2

• D. Reflection across the x-axis, dilation using k = ½

Multiple Choice

14. Use the figure to the right to find the value of $$x\degree$$ and $$y\degree$$ .

• A. $$x\degree=120\degree,\ y\degree=60\degree$$

• B. $$x\degree=80\degree,\ y\degree=100\degree$$

• C. $$x\degree=60\degree,\ y\degree=120\degree$$

• D. $$x\degree=100\degree,\ y\degree=80\degree$$

Multiple Choice

15. Line P ∥ Line Q and are cut by transversal R. Given that 𝑚∠1= $$35\degree$$ ,

which statement below is true?

• A. 𝑚∠2= $$35\degree$$

• B. 𝑚∠3= $$35\degree$$

• C. 𝑚∠5= $$145\degree$$

• D. 𝑚∠7= $$145\degree$$

Multiple Choice

16. Consider the triangles to the left. Which statement is true?

• A. The triangles are congruent because of angle-angle criterion

• B. The triangles are similar because of angle-angle criterion

• C. The triangles are neither similar nor congruent because angle-angle criterion has not been met

• D. There is not enough information to determine similarity or congruence.