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Properties of a Parallelogram - In a Parallelogram, Opposite Angles Are Equal.

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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.

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