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.

Algebra ->  Geometry-proofs -> 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.      Log On


   

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(20855) About Me  (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: WZ congruent to XY and WX congruent to ZY
Prove: the quadrilateral +XYZW is a parallelogram
proof:
let angle ZX+W => angle 1, angle ZX+Y => angle 4, Y+Z+X => angle 2, and W+Z+X => angle 3

Statements: …………………………………………….............................Reasons:

1. WZ+congruent to XY and WX congruent to ZY………….... 1. Given

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

3. DXYZ congruent to DZWX…………………............................... 3. SSS Postulate

4.<1 congruent to <2, and <3 congruent to <4………………….4. corresponding parts of congruent triangles are congruent
5. WZ || XY and WX+||+ZY+.......................................................... 5. If two lines are cut by a transversal so that alternate interior angles are congruent , the lines are ||.