Transformations, Similarity, and Congruence

Which one of the following would prove that two triangles are congruent?

• equal areas

• equal perimeters

• corresponding side lengths are equal

• corresponding angle measures are equal

Which transformation to a polygon could result in a polygon that is similar but not congruent to the original?

• dilation

• reflection

• rotation

• translation

Quadrilateral ABCD has been reflected vertically. The reflection is Quadrilateral EFHG. Which of the following pairs of sides are congruent?

• AB and EF

• AB and HG

• AD and EF

• AD and FG

A triangle has vertices A(−3, 6), B(−3, 4), and C (3, 4). If the triangle is translated 2 units to the right and 1 unit down, what will be the new coordinates of vertex A?

• (−1, 5)

• (−2, 4)

• (−5, 5)

• (−4, 4)

Quadrilateral ABCD is rotated 90 degrees clockwise and the result is quadrilateral PQRS. Which of the following sides on Quadrilateral PQRS is congruent to side AB on Quadrilateral ABCD?

• side PQ

• side QR

• side RS

• side SP

Which of the following transformations would result in two congruent triangles?

• vertex x should be moved up five units

• vertex x should be moved down 10 units

• vertex y should be moved left four units

• vertex z should be moved left four units

Students were asked to change the following figure through reflection and translation. Four students turned in their work for review. Which student was able to successfully complete the task?

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In addition to translation, what other transformation(s) would Parallelogram A require to exhibit congruence to

Parallelogram B?

• horizontal reflection

• 90˚ rotation to the right

• horizontal reflection and a 90˚rotation to the left

• horizontal reflection and a 90˚rotation to the right

Triangle A and Triangle B are congruent. Which series of transformations would take Triangle A to Triangle B?

• rotation 90˚counterclockwise about the vertex “x,” and translation up 3 and to the right 12

• rotation 90˚ counterclockwise about the vertex “x,” and translation up 3 and to the left 12

• rotation 90˚ counterclockwise about the vertex “x,” and translation down 3 and to the right 12

• rotation 90˚ counterclockwise about the vertex “x,” and translation down 3 and to the left 12

Triangle A is congruent to Triangle B. What sequence would transform Triangle A to Triangle B?

• vertical reflection, then a 45˚ clockwise rotation

• horizontal reflection, then a 135˚ counterclockwise rotation

• horizontal reflection, then vertical reflection, then 90˚ clockwise rotation

• vertical reflection, then horizontal reflection, then 90˚ counterclockwise rotation