In this chapter we will prove that ” in parallelogram, opposite sides are equal “.

This is very important property so make sure you remember it for your exam.

**Given:**

ABCD is a parallelogram in which opposite sides are parallel to each other.

AB || CD and AD || CB

**To Prove:**

Prove that opposite sides are equal in length.

AB = CD and AD = CB

**Proof:**

AB & CD are parallel lines intersected by transversal AC.

∠CAB = ∠ACD ( alternate angle )

∠CAD = ∠ACB ( alternate angle )

Now consider triangle ABC and ADC;

∠CAB = ∠ACD ( alternate angle )

AC = CA ( common side )

∠CAD = ∠ACB ( alternate angle )

By **ASA congruency**, both the triangles are congruent.

So, \mathtt{\triangle ABC\ \cong \triangle ADC}

Since both triangles are congruent, we can say that;

AB = CD and AD = CB

Hence Proved.