Question

Question 104

State whether the statement is True or False.

If the hypotenuse and an acute angle of one right-angled triangle are equal to the hypotenuse and an acute angle of another right-angled triangle, then the triangles are congruent.

Answer 1

True

In $\Delta ABC$ and $\Delta PQR$,
$\angle B=\angle Q={90}^{\circ }$
$\angle C=\angle R$ [given]
$\Rightarrow \angle A=\angle P$[Since if two angles of one triangle is equal to the two angles of another triangle ,then their third angle will also be equal]
Now, in $\Delta ABC$ and $\Delta PQR$,
$\angle A=\angle PAC=PR\angle C=\angle R$
By ASA congruence criterian, $\Delta ABC\cong \Delta PQR$