Question

Given: EB = BD, AE = CB, $\angle A=\angle C={90}^{\circ }$
Which congruence criterion do you use to prove $\Delta ABE\cong \Delta CDB$?

• A. ASA Congruence Criterion
• B. SAS Congruence Criterion
• C. RHS Congruence Criterion
• D. SSS Congruence Criterion

Answer 1

The correct option is C RHS Congruence Criterion

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

$EB=BD$ [Given]

$AE=CB$ [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.

$\therefore \Delta ABE\cong \Delta CDB$ by RHS congruence criterion.