Question

Which congruence criterion do you use in the following?
Given: EB = BD, AE = CB, $\angle A=\angle C={90}^{\circ }$

Answer 1

In $\Delta AEB$ and $\Delta CBD$,

$EB=BD$ [hypotenuse]

$AE=CB$ [Given]

$\angle A=\angle C={90}^{\circ }$ [Given]

Hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of another right-angled triangle.

$\therefore \Delta ABE\cong \Delta CDB$ [RHS congruence criterion]