Question

In these two triangles $QM\cong QP$, $QN$ $is$ a median of side $MP$. Can $\Delta QMN$ be congruent to $\Delta QPN$?

• A. Insufficient data
• B. Yes
• C. No
• D. Irrelevent

Answer 1

The correct option is B Yes

In $\Delta QMN$ and $\Delta QPN$

$\overline{QM}=\overline{QP}$ (given)

$\overline{QN}=\overline{QN}$ (common)

$\overline{MN}=\overline{NP}$ ($QN$ is a median of side $AC$)

$\therefore \Delta QMN\cong \Delta QPN$ ( SSS congruency Theorem)

Therefore, B is the correct answer.