1. Bastian was able to map △ABC onto △DEF using a reflection, rotation, and a dilation. Then Bastian concluded that the two triangles are similar because he was able to use a sequence of rigid transformations and dilations to map △ABC on to △DEF . What error did Bastian make in his conclusion?
A. Bastian used a rotation, so the triangles aren't similar.
B. There is no error. This is a correct conclusion.
C. Bastian used a combination of similarity transformations, which can produce a non-similar result.
D. Bastian used a dilation, which does not preserve similarity.
2. Which series of transformations will create similar but not congruent figures?
A. reflection and translation
B. reflection and dilation
C. reflection and rotation
D. rotation and translation
3. Fill in the blanks to make the following sentence true.
The similarity between triangles can be established if corresponding sides are------------- and if corresponding angles are-----------
Proportional
Congruent
4. If two figures are similar, can you conclude that the corresponding angles are congruent? Why or why not?
A. No, the corresponding angles are not congruent because dilations do not preserve angle measures.
B. Yes, the corresponding angles are congruent because rigid motions and dilations preserve angle measures.
C. No, the corresponding angles are not congruent because rigid motions and dilations do not preserve angle measures.
D. Yes, the corresponding angles are congruent because rigid motions and dilations preserve angle and length measures.
5. Are dilations the only transformations that result in figures that are similar? Explain
A. Yes, rigid motions like reflections result in figures that are not similar.
B. Yes, rigid motions result in figures that are congruent, not similar.
C. No, rigid motions like translations result in figures that are congruent and therefore similar.
D. No, rigid motions are the only transformations that result in figures that are similar.
1. C. Bastian used a combination of similarity transformations, which can produce a non-similar result.
2. B. reflection and dilation
3. Proportional, Congruent
4. A. No, the corresponding angles are not congruent because dilations do not preserve angle measures.
5. C. No, rigid motions like translations result in figures that are congruent and therefore similar.