Question

select the correct answer.
can triangle a be mapped onto triangle b using rigid transformations?
a. there is no possible sequence of transformations that can map triangle a onto triangle b.
b. triangle a can be mapped onto triangle b by rotating and then dilating triangle a.
c. triangle a can be mapped onto triangle b by reflecting triangle a.
d. triangle a can be mapped onto triangle b by rotating and then translating triangle a.

Explanation:

Rigid transformations (reflection, rotation, translation) preserve side lengths and angles, keeping triangles congruent. Triangle A and B are congruent: both are right triangles, with one pair of matching marked sides and the right angle. Reflection of triangle A will align the corresponding marked sides and right angle, mapping it onto triangle B. Option A is wrong because a mapping exists. Option B is wrong because dilation is not a rigid transformation. Option D is wrong because rotation/translation alone won't align the mismarked sides; reflection is needed.

Answer:

C. Triangle A can be mapped onto triangle B by reflecting triangle A.