#### theorem

**Theorem:** In a parallelogram, opposite sides are equal.

AB = CD and BC = DA**Proof:** Let AC be the diagonal of parallelogram. consider two ∆ABC and ∆ CDA

∠CAB = ∠ACD ....(1) (Alternate interior angles)

∠ACB =∠ CAD ...(2) (Alternate interior angles)

And , AC = CA ...(3) (common side)

From condition 1,2 and 3

∆ABC ≅ ∆ CDA (By ASA congruence rule)

Hence as triangles are congruent triangles, the corresponding sides are equal,

So , AB = CD (C.P.C.T)

BC = DA (C.P.C.T)

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

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