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.