Question

in the following figure ABCD represent a rectangle prove that triangle ABC congruence to triangle triangle DCB​

Answer 1

TRIANGLES

We're asked to prove that ∆ABC is congruent to ∆DCB when ABCD is a rectangle and AC and BD are its diagonals.

How do you know two triangles are congruent? "Two triangles are said to be congruent if any three among their corresponding sides and corresponding angles are equal in measure". $\:$

Let's start with our answer!

Carefully look into the first diagram. Both the triangles ABC and DCB are formed with a same base BC. Since it is common in both the triangles, we can say that BC = BC.

*Whenever two triangles embedded into or as a quadrilateral, split and draw them. It helps you understand better. And it's not necessary to do everytime if you are good enough using a single reference.

We know that the opposite sides of a rectangle are parallel and equal. So, AB = DC. Also, the angles of formed at the vertices are of 90° each. So, it can be written that ∠B = ∠C.

We've three corresponding, equal parts in triangles ABC and DCB.

• BC = BC (Side)
• ∠B = ∠C (Angle)
• AB = DC (Side)

∆ABC ≅ ∆DCB by SAS congruence rule. Hence, proved!