Question

Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.

Answer 1

- Let $\triangle ABC$ and $\triangle PQR$ be two triangles such that the sides $AB \parallel PQ$, $BC \parallel PR$, and $AD \parallel PM$.
- Since the corresponding sides are proportional, we can use the criteria for similarity of triangles:

$\frac{AB}{PQ} = \frac{BC}{PR} = \frac{AD}{PM}$

- Therefore, by the Side-Side-Side (SSS) similarity criterion, $\triangle ABC \sim \triangle PQR$.