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: Definition of Triangle Similarity:
Two triangles are similar if their corresponding angles are equal and the ratios of their corresponding sides are proportional.

Step 2: Provided Information:
It is given that:
\[ \frac{AB}{QR} = \frac{BC}{PR} \] This implies that the sides of the two triangles are proportional.

Step 3: Determining the Similarity Criterion:
For similarity, corresponding angles must also be equal.
Given proportional sides, similarity requires the angle included between these sides to be equal in both triangles.

Conclusion:
Consequently, the two triangles are similar if and only if:
\[ \angle B = \angle R \] This is the requisite condition for the similarity of triangles ABC and PQR.