Answer:
Triangles OPQ and NPR are similar by AA Similarity Postulate
Step-by-step 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
[tex]\frac{OP}{NP}=\frac{QP}{RP}[/tex]
substitute the values
[tex]\frac{175}{350}=\frac{215}{430}[/tex]
[tex]\frac{1}{2}=\frac{1}{2}[/tex] -----> is true
therefore
The triangles OPQ and NPR are similar
