Question

Proof that :A quadrilateral is a parallelogram if pair of opposite sides is equal and parallel​

Answer 1

Answer:

A is parallel to B

and D is equal to C

and it's a quadrilateral.

hence proved that A quadrilateral is a parallelogram if pair of opposite sides is equal and parallel.

Step-by-step explanation:

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Answer 2

Answer:

✌$\huge\underbrace{\mathtt\red{A} \mathtt\purple{N} \mathtt\green{S}\mathtt\blue{W} \mathtt\blue{E} \mathtt\orange{R}}$✌

Step-by-step explanation:

$\huge\red{\underline\orange{\underline\purple{\textsf{Theorm:}}}}$

A quadrilateral is a parallelogram if pair of opposite sides is equal and parallel.

In a parallelogram, opposite angles are equal.

$\huge\red{\underline\orange{\underline\purple{Proof:}}}$

First, we assume that ABCD is a parallelogram.

Compare ΔABC and ΔCDA once again:

AC=AC (common sides)

∠1=∠4 (alternate interior angles)

∠2=∠3 (alternate interior angles)

Thus, the two triangles are congruent, which means that

∠B=∠D

Similarly, we can show that

∠A=∠C

This proves that opposite angles in any parallelogram are equal.

Hence, A quadrilateral is a parallelogram if pair of opposite sides is equal and parallel.