Question

Question 86

State whether the statement is True or False.

In the given figures, two triangles are congruent by RHS.

Answer 1

In $\Delta ABC,AC=\sqrt{A{B}^2+B{C}^2}=\sqrt{4^2+5^2}=\sqrt{41}cm$ [by Pythagoras theorem]
In $\Delta PQR,PR=\sqrt{P{Q}^2+Q{R}^2}=\sqrt{4^2+5^2}=\sqrt{41}cm$ [by Pythagoras theorem]
Now, in $\Delta ABC$ and $\Delta PQR$,
AB = PQ = 4 cm
$AC=PR=\sqrt{41}cm\angle ABC=\angle PQR={90}^{\circ }$
By RHS congruence criterian, $\Delta ABC\cong \Delta PQR$