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Question

Triangle upper A upper B upper C is drawn next to a smaller triangle, triangle upper M upper N upper P. The interior angles by vertices upper A and upper P are marked by single arcs and are given as 56 and 62 degrees, respectively.

Given two isosceles triangles, △ABC and △MNP, is △ABC similar to △MNP if ∠A=56° and ∠P=62°? If so, which criterion helps you prove this conclusion?

(1 point)
Responses which answer is correct and why

This does not matter because ∠A and ∠P are not corresponding angles.
This does not matter because angle upper A and angle upper P are not corresponding angles.

Yes, △ABC is similar to △MNP by the AA Criterion.
Yes, triangle upper A upper B upper C is similar to triangle upper M upper N upper P by the AA Criterion.

Yes, △ABC is similar to △MNP by the SSS Criterion.
Yes, triangle upper A upper B upper C is similar to triangle upper M upper N upper P by the SSS Criterion.

No, △ABC is not similar to △MNP because ∠A=56° is not equal to ∠P=62°.
No, triangle upper A upper B upper C is not similar to triangle upper M upper N upper P because angle upper A equals 56 degrees is not equal to angle upper P equals 62 degrees .
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Answer 1

To determine if Triangle ABC is similar to Triangle MNP, we need to use the information provided about the angles. We know that:

• ∠A = 56°
• ∠P = 62°

Since the two angles are not equal, they cannot correspond to each other in two similar triangles. For triangles to be similar, they must have angles that are equal or at least have the same angle measures.

Thus, the correct response is:

No, △ABC is not similar to △MNP because ∠A=56° is not equal to ∠P=62°.
No, triangle A B C is not similar to triangle M N P because angle A equals 56 degrees is not equal to angle P equals 62 degrees.