Which theorem can be used to prove that the two triangles are congruent?

Solution:

When two triangles are put on each other and are exactly the same in shape and size. they are called congruent triangles. The symbol of congruence is '≅'.

The congruent triangles are exactly the same with respect to their shape and size. Thus, all corresponding parts of congruent triangles are also congruent.

Let △ ABC and △ PQR be two triangles, if ∠A = ∠P, AB = PQ and  ∠B = ∠Q

Then △ ABC ≅ △ PQR by Angle Side Angle (ASA) rule.

Similarly, let △ ABC and △ XYZ be two triangles, if  BC = YZ, ∠C = ∠Z and  AC = XZ

Then △ ABC ≅ △ XYZ by Side Angle Side (SAS) rule.

Similarly, let △ ABC and △ DEF be two triangles, if  AC = DE, BC = FE and AB = DF

Then △ ABC ≅ △ DEF by Side Side Side (SSS) rule.

Similarly, let △ ABC and △ LMN be two right triangles, if  ∠B = ∠M = 90º, AC = LN (Hypotenuse) and AB = LM (side)

Then △ ABC ≅ △ LMN by Right-Angle Hypotenuse Side (RHS) rule.

Thus, the congruence of the triangle can be proved by ASA, SAS, SSS, and RHS rules.

Which theorem can be used to prove that the two triangles are congruent?

Summary:

The congruence of the triangle can be proved by ASA, SAS, SSS, and RHS rules.