This is the first of a series of post about the conditions of a quadrilateral to be a parallelogram. In this post, I will be discussing the proof that if the opposite sides of a quadrilateral are congruent, then it is a parallelogram.

**Given**

Quadrilateral

**Proof**

Draw diagonal .

Now, (S) and (S).

Also, a segment is congruent to itself (Relfexive Property), so (S).

Therefore, by the SSS Triangle Congruence, .

Since corresponding angles of congruent triangles are congruent,

and .

But these pairs of angles are corresponding angles, so by the **Parallel Line Postulate**,

and .

So, quadrilateral is a parallelogram.

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