Question

hüseyin was able to map quadrilateral efgh onto ejgk using a vertical stretch.
hüseyin concluded:
\i was able to map quadrilateral efgh onto quadrilateral ejgk 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 arent 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 type of dilation (a non - rigid transformation that changes the size of the figure). Rigid transformations (like translations, rotations, reflections) preserve the size and shape of a figure, while dilations change the size (scale factor not equal to 1) but preserve the shape.
2. Similar vs. Congruent Figures:

• Similar figures have the same shape but not necessarily the same size. They can be mapped onto each other using a sequence of rigid transformations and dilations.
• Congruent figures have the same shape and size and can be mapped onto each other using only rigid transformations.
• In this case, Hüseyin used a vertical stretch (a dilation) along with rigid transformations to map \(EFGH\) onto \(EJGK\). This means the figures have the same shape but different sizes, so they should be similar. However, let's re - evaluate the options:
• Option A: A vertical stretch (a type of dilation) is a valid transformation for showing similarity. So this option is incorrect.
• Option B: The figures are not congruent because a dilation (vertical stretch) was used, which changes the size. So this option is incorrect.
• Option C: Hüseyin's conclusion is correct. He used a sequence of rigid transformations (implicit in the mapping, even though he mentioned a vertical stretch which is a dilation) and the combination of rigid transformations and dilations is the correct way to show similarity. The vertical stretch is a dilation, and when combined with rigid transformations, it shows that the figures have the same shape (due to rigid transformations preserving shape and dilation preserving shape while changing size), so the figures are similar.

Answer:

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