Question

in a parallelogram prove that the opposite sides are equal and opposite angles are equal diagonals bisect each other

Answer 1

Statement : In a parallelogram, opposite angles are equal.

Given : Parallelogram ABCD

To prove ; ∠A = ∠C and ∠B = ∠D

Proof :

In parallelogram ABCD,
Consider,

AD || BC and AB is transversal

∠A + ∠B = 180° [Co - int. Angles]...... (i)

Now, consider AB || DC and BC transversal

∠B + ∠C = 180° [Co - int. Angles]...... (ii)

From (i) and (ii) we get ;

∠A + ∠B = ∠B + ∠C
∠A = ∠C
∠B = ∠D

Hence, it is proved.