#### theorem

**Theorem:** In a parallelogram, opposite angles are equal.**Proof :** In parallelogram ABCD , AB || DC and DA intersects them. Therefore, ∠A + ∠D = 180° (Consecutive interior angles) ... (1)

Again , in parallelogram ABCD , AD || BC and AB intersects them

`therefore` ∠A +∠B = 180° (Consecutive interior angles) ..(2)

From (1) and (2) , we get

∠A + ∠D = ∠A + ∠B = 180°

`=>` ∠D = ∠B

`=>` ∠B = ∠D

Similarly , ∠A + ∠C

Hence , ∠A + ∠C and ∠D= ∠B.

#### Shaalaa.com | Theorem : In a parallelogram, opposite angles are equal.

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