Question

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

Answer 1

Answer:

As per ASA postulate, the two triangles are congruent.

Step-by-step explanation:

We are given two triangles:

$\triangle ABC$ and $\triangle DEC$.

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 $\angle B$ and $\angle E$ are alternate angles $\Rightarrow$ $\angle B = \angle E$.

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.

$\Rightarrow \angle ACB = \angle DCE$

Also, it is given that AD bisects BE.

i.e. EC = CB

1. $\angle B = \angle E$

2. EC = CB

3. $\angle ACB = \angle DCE$

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

Hence, proved that $\triangle ABC$ $\cong$ $\triangle DEC$.