SOLUTION: Can you please help me! Prove: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a paralellogram. I started it by saying: Given: A

Question 276811: Can you please help me!
Prove: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a paralellogram.
I started it by saying:
Given: Angle B is congruent to Angle D.
and Angle A is congruent to Angle C.
Prove: ABCD is a paralellogram.
Thank you so much!!!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The trick is to realize that the sum of the measures of the interior angles of any quadrilateral is 360�. So, if you have two congruent angles that each measure

� and two other congruent angles that each measure

�, then the following equation must hold:

But if you divide by 2:

So now if you extend the sides of your quadrilateral past the vertices, then you can show that you have equal measure opposite interior angles formed by a transversal meaning that you have parallel lines.

John

RELATED QUESTIONS
Can you please help me with this proof? Thanks. Prove: If both pairs of opposite... (answered by solver91311)

Prove that if both pairs of opposite sides of a quadrilateral are congruent, then the... (answered by ikleyn)

How do you prove the following theorem. If both pairs of an opposite sides of a... (answered by MathLover1)

Could you please help me solve this problem? Prove that if all the sides of a convex... (answered by jim_thompson5910)

Can you prove if the quadrilateral is a parallelogram then opposite sides of a... (answered by venugopalramana)

can you please help me with this problem <<<< write a proof about of Theorem 6-6 >>>>>... (answered by Mathtut)

Can you please help me with the following problem <<<<< write a paragraph proof for... (answered by Mathtut)

Write a proof argument for part (b) of the sufficient conditions for a parallelogram... (answered by scott8148)

Please help me with this problem! "Draw a diagram, provide the given and conclusion,... (answered by richwmiller)