Question

Which triangles are similar?
Justify your reasoning

Answer 1

Triangles OPQ and NPR are similar by AA Similarity Postulate

Explanation:

we know that

In this problem

NR is parallel to OQ

therefore

Triangles OPQ and NPR are similar by AA Similarity Postulate (the three internal angles are congruent)

because

<RNP=<QOP -----> by corresponding angles

<NRP=<OQP ----> by corresponding angles

<NPR=<OPQ

Remember that

If two triangle are similar, then the ratio of its corresponding sides is equal

Verify

`(OP)/(NP)=(QP)/(RP)`

substitute the values

`(175)/(350)=(215)/(430)`

`(1)/(2)=(1)/(2)` -----> is true

therefore

The triangles OPQ and NPR are similar