Question

If in triangles $ABC$ and $PQR$, $\frac{AB}{QR} = \frac{BC}{PR}$, then they will be similar, when:

• A. $\angle B = \angle Q$
• B. $\angle A = \angle R$
• C. $\angle B = \angle R$
• D. $\angle C = \angle Q$

Answer 1

Answer: (C)

$\angle B = \angle R$

Answer 2

For two triangles to be similar by the SAS (Side-Angle-Side) criterion:
The corresponding sides must be proportional.
The included angles must be equal.
Here, the included angles are $\angle B$ in $\triangle ABC$ and $\angle Q$ in $\triangle PQR$. Thus:
$\angle B = \angle Q$