Question

Ananya is designing the window shown in the figure. She wants to make $△$PRQ congruent to $△$PRS. She designs the window so that PR $\perp$ QS. Which of the following conditions will make the two triangles congruent?

• A. RQ = RS
• B. PQ = PS
• C. Both (A) and (B)
• D. None of these

Answer 1

Answer: (C)

Both (A) and (B)

In $△PQS$

$\Rightarrow$ $PR\perp QS$

$\Rightarrow$ So, $△PRQ$ and $△PRS$ are right angled triangle.

$\Rightarrow$ $\angle PRQ=\angle PRS={90}^o$ [Given]

$\Rightarrow$ If $PQ=PS$ and $RQ=RS$ then, by $RHS$ property $△PRQ\cong △PRS$.

$\Rightarrow$ So, both condition in Option A and B required to make $△PRQ\cong △PRS$