Question

The triangles are similar. Write a Similarity statement for the triangles

Answer 1

c

Explanation:

big small

nqr npm

Answer 2

Third option.

`\triangle NPM \sim \triangle NQR`

Explanation:

By given, we know that both triangles are similar, that means their sides are proportional and their angle are congruent. However, we need to be careful when we write the similarity statement, because all corresponding vertex must be in the same position.

For example, from the image, we can deduct that the similarities are

`\triangle NPM \sim \triangle NQR\\\triangle PMN \sim \triangle QRN\\\triangle MNP \sim \triangle RNQ\\\triangle NMP \sim \triangle NRQ`

Each statement is true, based on the similarity provided by the problem.

Now, let's see which option has one of this similarities.

You can observe that the first option is not the right answer because, the triangle NPM doesn't correspond to triangle RNQ.

Similarly, the second choice is not correct, because triangle NPM is no similar to triangle NRQ.

However, the third choice is the right answer, because triangle NPM corresponds to triangle NQR, they are similar.

Therefore, the right answer is the third choice:
`\triangle NPM \sim \triangle NQR`