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, \( \triangle ABC \sim \triangle PQR \).