Question

In the given figure, AD = BC. $\Delta ABC\cong \Delta ADC$ by which of the following criterian?

Answer 1

Given, AD = BC (side)
AC = AC (common side and hypotenuse)
and $\angle$ADC = $\angle$ABC = 90${}^{\circ }$ (Given)

Therefore, $\Delta ABC\cong \Delta ADC$ by RHS congruency

RHS (Right Angle-Hypotenuse-Side) Congruency:
Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and the corresponding side of the other triangle.