In Fig. 6.33, $CM$ and $RN$ are medians of $ riangle ABC$ and $ rian…

Question

In Fig. 6.33, $CM$ and $RN$ are medians of $	riangle ABC$ and $	riangle PQR$ respectively, and $	riangle ABC \sim 	riangle PQR$. Which statement is correct?

![](https://qallery.app/diagrams/v2_70b17897d87b/img-048.jpeg)

Accepted Answer

A. $	riangle AMC \sim 	riangle PNR$ by SAS similarity

Since $	riangle ABC \sim 	riangle PQR$, we have $\frac{AB}{PQ}=\frac{CA}{PR}$ and $\angle A=\angle P$. As $CM$ and $RN$ are medians, $AB=2AM$ and $PQ=2PN$, so $\frac{AM}{PN}=\frac{CA}{PR}$. With the included angle $\angle MAC=\angle NPR$, this gives $	riangle AMC \sim 	riangle PNR$ by SAS. Option D is incorrect because the result proved is $\frac{CM}{RN}=\frac{AB}{PQ}$, not $\frac{BC}{PQ}$.

Answer

$	riangle AMC \cong 	riangle PNR$ by SAS congruence

Answer

$	riangle CMB \sim 	riangle RNQ$ by AA similarity only

Answer

$\frac{CM}{RN}=\frac{BC}{PQ}$

In Fig. 6.33, $CM$ and $RN$ are medians of $\triangle ABC$ and $\triangle PQR$ respectively, and $\triangle ABC \sim \triangle PQR$. Which statement is correct? ![](https://qallery.app/diagrams/v2_70b17897d87b/img-048.jpeg)