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

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 horizontal reflection, then 90˚ counterclockwise rotation

vertical reflection, then a 45˚ clockwise rotation

horizontal reflection, then a 135˚ counterclockwise rotation

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

Triangle ABC is congruent to Triangle PQR. What sequence of transformations for Triangle ABC results in Triangle PQR?

rotation 90˚ counterclockwise about point X , 13 units right

rotation 90˚ counterclockwise about vertex A, and 8 units down

rotation 90˚ counterclockwise about vertex B, 8 units right

rotation 90˚ counterclockwise about vertex B, 16 units right

What series of transformations to Rectangle ABCD would result in Rectangle PQRS ?

rotation 90˚ clockwise about vertex C , then translate 4 units to the right

rotation 90˚ clockwise about vertex B, then translate 8 units to the right

rotation 90˚ clockwise about vertex B, then translate 16 units to the right

rotation 90˚ clockwise about vertex C , then translate 12 units to the right

Figure A is an irregular polygon. When Figure A is dilated 50% then rotated 270 degrees clockwise about the origin, it creates Figure B. After the series of transformations, which image could show how Figure B is positioned in relation to Figure A?

Figure B is closer to the origin, is turned on a different side, and is in a different quadrant than Figure A.

Figure B is closer to the origin and is in a different quadrant than Figure A.

Figure B is closer to the origin but is in the same quadrant than Figure A.

Figure B is turned on a different side length but is in the same quadrant than Figure A.

According to the angle-angle criterion, are these two triangles similar?

No, both triangles do not have the same angle measures.

Yes, both triangles have a 75˚ angle.

Yes, both triangles angle measures add up to 180˚.

No, the angle measures do not add up to 180˚.

A parallelogram is formed by the points A (2, 4), B (6, 3), C (0,0), and D (4, 1). What transformation could have occurred in order for A’ to be (3, 6)?

Reflection across the axis y = 5

Rotation of 90° about the origin

Translation following the rule (x + 2, y + 1)

Which of the following statements would be TRUE if Line A is parallel to Line B?

m∠4 = m∠8 because they are alternate interior angles

m∠1 = m∠6 because they are alternate exterior angles

m∠4 = m∠10 because they are alternate interior angles

m∠2 = m∠14 because they are alternate exterior angles

Are these triangles similar triangles?

Yes, they are similar according to the Angle-Angle criterion.

Yes, they are similar according to Angle Side Angle postulate.

No, they cannot be similar because the side lengths are not equal.

No, they are congruent according to the Angle Side Angle Postulate.

Which statements would be TRUE if Line A is parallel to Line B?

m∠2 = m∠7 because they are alternate exterior angles

m∠1 = m∠7 because they are alternate exterior angles

m∠1 = m∠5 because they are alternate interior angles

m∠2 = m∠7 because they are alternate interior angles

Figure A is doubled in size then reflected across the x-axis creating Figure B. How will the coordinates of Figure B differ from Figure A as a result of this series of transformations?

two times the x-value and two times the opposite y-value

the opposite x-value and two times the y-value

two times the x-value and two times y-value

two times the opposite x-value and the opposite y-value

Triangle A and Triangle B are similar right triangles. Figure A has been rotated 90 degrees clockwise about the origin and reflected across the y-axis. Which set of coordinates could represent this series of transformations if the Triangle B is also twice the size of Triangle A?

A (1, 1), B (3, 1), C (1, 4) à A’ (2, -2), B (-3, -1), C (-8, -2)

A (1, 1), B (3, 1), C (1, 4) à A’ (2, -2), B (-3, 1), C (-2, 8)

A (1, 1), B (3, 1), C (1, 4) à A’ (2, -2), B (1, -3), C (8, -2)

A (1, 1), B (3, 1), C (1, 4) à A’ (2, -2), B (6, -2), C (2, -8)

Two of the angle measures for two triangles are given. Triangle A: m∠1 = 45˚, m∠2 = 45˚ Triangle B: m∠1 = 45˚, m∠2 = 90˚According to the angle-angle criterion, are these two triangles similar?

Yes, the m∠3 = 90˚ for Triangle A.

Yes, the m∠1 = 45˚ for both triangles.

No, both triangles do not have the same angle measures.

No, the angle measures do not add up to 180˚.

Congruence and Similar Transformations

Authored by Barbara White

Mathematics

8th Grade

CCSS covered

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28 questions

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Tags

CCSS.8.G.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

dilation

reflection

rotation

translation

Tags

CCSS.HSG.SRT.A.2

CCSS.8.G.A.4

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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?

Tags

CCSS.8.G.A.3

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Congruence and Similar Transformations

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

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

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

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?

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?

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

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?

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

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

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

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