Question

For the given diagram above,

• A. $△PRQ\cong △ABC$
• B. $△PRQ\cong △ACB$
• C. $△PRQ\cong △CAB$

Answer 1

The correct option is A $△PRQ\cong △ABC$

Here we have two right triangles $PRQ$ and $ABC$
And $RQ=BC=3$ cm
Applying pythagorean theorem for $\Delta PRQ$:
$P{Q}^2=P{R}^2+R{Q}^2$
$\Rightarrow P{Q}^2=4^2+3^2=9+16=25$
$\Rightarrow PQ=\sqrt{25}=5$ cm
$\Rightarrow PQ=AC$
$\therefore$ By Hypotenuse Leg theorem, both the right angles are equal.
$\Rightarrow \Delta PRQ\cong \Delta ABC$