Sides AB and BC and median AD of triangle ABC are respectively proportional to sides PQ and QR and median PM of $ riangle PQR$. Show that $ riangle ABC \sim riangle PQR$.

Question

Sides AB and BC and median AD of triangle ABC are respectively proportional to sides PQ and QR and median PM of $	riangle PQR$. Show that $	riangle ABC \sim 	riangle PQR$.

Accepted Answer

Step 1: Correct figure.
Step 2: In $	riangle ABD$ and $	riangle PQM$:
$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AD}{PM}$ (given)
$\frac{AB}{PQ} = \frac{2BD}{2QM} = \frac{AD}{PM}$
$\frac{AB}{PQ} = \frac{BD}{QM} = \frac{AD}{PM}$
Step 3: $	herefore 	riangle ABD \sim 	riangle PQM$ (SSS similarity)
Step 4: $	herefore \angle B = \angle Q$
Step 5: In $	riangle ABC$ and $	riangle PQR$:
$\frac{AB}{PQ} = \frac{BC}{QR}$ and $\angle B = \angle Q$
$	riangle ABC \sim 	riangle PQR$ (SAS similarity)

Question

Solution