Question

In the given figure, in order to prove $△ABC\sim △PQR$ by SAS property, which of the following condition is required?
Given: $\angle B=\angle Q$

• A. $\frac{AB}{PQ}=\frac{BC}{QR}$
• B. $\frac{AB}{PQ}=\frac{AC}{PR}$
• C. $\frac{BC}{QR}=\frac{AC}{PR}$
• D. None of the above

Answer 1

The correct option is A $\frac{AB}{PQ}=\frac{BC}{QR}$

When the triangles are similar by the SAS property, two corresponding sides are in proportion and the including angles are equal in measure.


Here, $\angle B=\angle Q$

So, the sides related to the angle $\angle B$ are $AB\text{and}BC$ and for the angle $\angle Q$ are $PQ\text{and}QR$.

Hence, required condition is $\frac{AB}{PQ}=\frac{BC}{QR}$.
$\therefore$ Correct option is $\left(a\right).$