Congruency and similarity

Which of the following transformations results in SIMILAR (not congruent) figures?

• translation

• reflection

• rotation

• dilation

ABC has vertices (9,-3), (3,5) and (5,9) respectively.  Its image A’B’C’ has coordinates (-6,-3),(6,6) and (12,3). Which sequence of transformations can be applied to show the two triangles are similar.

• 270 CCW rotaton, followed by translation 7 left and 1 up, then dilaton using 3/2 as scale factor

• 90 CCW rotaton, followed by translation 7 right and 1 down, then dilaton using 2/3 as scale factor

• Translation 7 left and 1 up, followed by 270 CCW rotation, then dilaton using 3/2 as scale factor

• Translation 7 right and 1 up, followed by 90 CCW rotation, then dilaton using 2/3 as scale factor

Which transformation creates similar, but not congruent, figures?

• Rotations

• Dilations

• Reflections

• Translation

What series of transformations occurred?

• Translation Left 2, Dilation by 3

• Translation Left 3, Dilation by 2

• Reflection over y-axis, Dilation by 2

• Reflection over y-axis, Dilation by 1/2

Choose the statement that accurately describes the relationship between ABCD and EFGH.

• ABCD and EFGH are congruent, but not similar.

• ABCD and EFGH are similar, but not congruent.

• ABCD and EFGH are both congruent and similar.

• ABCD and EFGH are neither congruent, nor similar.

Answer explanation

The figures are similar, because they have congruent corresponding angles and proportional corresponding side lengths.

They are not congruent, because they are not the same size (the corresponding side lengths are not congruent/equal).

Determine if the two figures are similar by using transformations.

• similar; a reflection and a dilation map one figure onto the other.

• similar; a rotation and a dilation map one figure onto the other.

• similar; a translation and a dilation map one figure onto the other.

• The figures are not similar.

Describe the similarity transformation that maps to (dilations have a center at the origin).

• a dilation with a scale factor of 2 followed by a translation 4 units right and 3 units down.

• a dilation with a scale factor of 1 / 2 followed by a translation 4 units left and 3 units up.

• Translation 4 units right and 3 units down followed by a dilation with a scale factor 2.

• Translation 4 units left and 3 units up followed by a dilation with a scale factor 1 / 2.

Determine a series of transformations that would map polygon ABCD onto polygon A'B'C'D'?

• reflection over the x - axis followed by a dilation centered at the origin with a scale factor of 1/3

• reflection over the x-axis followed by a dilation centered at the origin with a scale factor of 3

• rotation of 90 degrees clockwise followed by a dilation centered at the origin with a scale factor of 1/3

• rotation of 90 degrees clockwise followed by a dilation centered at the origin with a scale factor of 3

Which transformation(s) create(s) similar figures?

• Dilation

• Translation, Reflection, and Rotation

• Translation and Reflection

• Reflection and Rotation

Figures A and B are similar.  Which transformation of figure A shows that A and B are similar?

• Translation 3 units up
• Translation 3 units down
• Dilation by a scale factor of 3
• Dilation by a scale factor of 1/3