Given: AB || DE , AD bisects BE.
Prove: ABC = DEC using the ASA postulate.

As per ASA postulate, the two triangles are congruent.

Step-by-step explanation:

We are given two triangles:

and .

AD bisects BE.

AB || DE.

Let us have a look at two properties.

1. When two lines are parallel and a line intersects both of them, then alternate angles are equal.

i.e. AB || ED and and are alternate angles .

2. When two lines are cutting each other, angles formed at the crossing of two, are known as Vertically opposite angles and they are are equal.

Also, it is given that AD bisects BE.

i.e. EC = CB

1.

2. EC = CB

3.

So, we can in see that in and , two angles are equal and side between them is also equal to each other.

Hence, proved that .