Question

hüseyin was able to map quadrilateral efgh onto rjgk using a vertical stretch.
hüseyin concluded:
\i was able to map quadrilateral efgh onto quadrilateral rjgk using a sequence of rigid transformations and dilations, so the figures are similar.\
what error did hüseyin make in his conclusion?
choose 1 answer:
a hüseyin used a vertical stretch, so the quadrilaterals aren’t similar.
b the quadrilaterals are mapped onto each other, so they are congruent, not similar.
c there is no error. this is a correct conclusion.

Explanation:

To determine the error in Hüseyin's conclusion, we analyze the transformation and the definitions of similar and congruent figures:

1. Understanding Transformations: A vertical stretch is a non - rigid transformation (a type of dilation with a scale factor in the vertical direction). However, when a figure is mapped onto another using a sequence of rigid transformations (which preserve shape and size) and dilations (which preserve shape but can change size), the figures are similar. Similar figures have the same shape, and their corresponding angles are equal, and corresponding sides are in proportion.
2. Analyzing Option A: A vertical stretch is a type of dilation. If a figure can be mapped to another using rigid transformations (translations, rotations, reflections) and dilations, the figures are similar. So, the statement in option A is incorrect.
3. Analyzing Option B: Congruent figures are a special case of similar figures where the scale factor of the dilation is 1 (i.e., no change in size). But here, a vertical stretch (a dilation with a scale factor not equal to 1 in the vertical direction) was used. So, the figures are not congruent, and this option is incorrect.
4. Analyzing Option C: Hüseyin used a sequence of rigid transformations and a dilation (vertical stretch) to map one quadrilateral to the other. By the definition of similar figures (figures that can be mapped to each other by a similarity transformation, which is a composition of rigid transformations and dilations), the figures are similar. So, there is no error in his conclusion.

Answer:

C. There is no error. This is a correct conclusion.