Question

In two right triangles, one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

Answer 1

Given : In $\Delta ABCand\Delta DEF,$

$\angle B=\angle E={90}^{\circ }$

$\angle C=\angle F$

$AB=DE$

To prove : $\Delta ABC\cong \Delta DEF$

Proof : In $\Delta ABCand\Delta DEF,$

$\angle B=\angle E(Each={90}^{\circ })\angle C=\angle F\left(Given\right)AB=DE\left(Given\right)\therefore \Delta ABC\cong \Delta DEF\left(AASaxiom\right)$