Question

in the figure shown, $\triangle mnp sim \triangle qrp$. list all pairs of congruent angles.
a) $angle m cong angle r$
b) $angle m cong angle q$
c) $angle n cong angle r$
d) $angle n cong angle q$
e) $angle p cong angle p$

Explanation:

Step1: Recall the property of similar triangles

For similar triangles \(\triangle MNP\sim\triangle QRP\), corresponding angles are congruent.

Step2: Identify corresponding angles

In \(\triangle MNP\) and \(\triangle QRP\), \(\angle M\) corresponds to \(\angle Q\), \(\angle N\) corresponds to \(\angle R\), and \(\angle P\) is common to both triangles (so \(\angle P\cong\angle P\) by reflexive property).

Answer:

B. \(\angle M\cong\angle Q\), C. \(\angle N\cong\angle R\), E. \(\angle P\cong\angle P\)