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

The Correct Option is C

Step 1: Understanding the concept of triangle similarity:
Two triangles are said to be similar if their corresponding angles are equal and the ratios of their corresponding sides are proportional.

Step 2: Given condition:
We are given that: \[ \frac{AB}{QR} = \frac{BC}{PR} \] This condition tells us that the ratios of the corresponding sides of the two triangles are proportional.

Step 3: Identifying the similarity condition:
For the two triangles to be similar, the corresponding angles must also be equal.
Since the sides are proportional, we need to show that the corresponding angles between the two triangles are equal.
This is satisfied when the angle between the two sides of the triangles is the same.

Conclusion:
Therefore, the two triangles will be similar if and only if: \[ \angle B = \angle R \] This is the necessary condition for the similarity of triangles ABC and PQR.