SOLUTION: How do you prove the following theorem. If both pairs of an opposite sides of a quadrilateral are congruent, then the Quadrilateral is a paralleogram.

Question 117575This question is from textbook
: How do you prove the following theorem.
If both pairs of an opposite sides of a quadrilateral are congruent, then the Quadrilateral is a paralleogram. This question is from textbook

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Theorem: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Given: congruent to and congruent to
Prove: the quadrilateral is a
proof:
let angle => angle , angle => angle , => angle , and => angle

: ��.............................:

1. congruent to and congruent to ��.... 1. Given

2. congruent to ...............................................................2. Reflexive property

3. congruent to ��............................... 3. SSS Postulate

4.< congruent to <, and < congruent to <��.4. corresponding parts of congruent triangles are congruent
5. || and ||.......................................................... 5. If two lines are cut by a transversal so that alternate interior angles are congruent , the lines are ||.

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