#### Question

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

#### Solution

Given that, in two right triangles one side and acute angle of one are equal to the corresponding side and angles of the other.

We have to prove that the triangles are congruent. Let us consider two right triangles such that

*∠B *= *∠**C *= 90° ........(1)

*AB *= *DE ........(2)*

*∠C *= *∠**F ........(3)*

Now observe the two triangles ABC and DEF

*∠.C *= *∠**F [From (3)]*

*∠B *= *∠**E [From (1)]*

and *AB *= *DE [From (2)]*

So, by AAS congruence criterion, we have

*ΔABC ≅* *Δ**DEF*

∴The two triangles are congruent Hence proved

Is there an error in this question or solution?

Solution In Two Right Triangles One Side an Acute Angle of One Are Equal to the Corresponding Side and Angle of the Othe Prove that the Triangles Are Congruent. Concept: Congruence of Triangles.