Question

Which postulate or theorem proves that these two triangles are congruent?

Answer 1

ASA postulate of congruence.

Explanation:

The ASA postulate refers to the congruence of Angle-Side-Angle pairs. In this problem we have ABE and DCE triangle. The reasons why we can use ASA postulate are:

• We can see that angles DEC and AEB are congruent, because they are opposite angles.
• Side AE is congruent with side DE, it's part of the hypothesis of the problem.
• Also, angle A is congruent with angle D, by hypothesis.

So, there are three pairs of congruence, Angle-Side-Angle. Therefore, according to ASA postulate, we can say that the triangle ABE is congruent with triangle DCE.

Answer 2

ASA postulate of congruency

Explanation:

Here Given AE=ED and ∠BAE=∠CDE

Also if we clearly observe ∠AEB=∠CED

By ASA postulate those two triangles are congruent.

The ASA (Angle,Side,Angle) postulate states that if two triangles with two angles and the included angle are equal then the two triangles are congruent.