SOLUTION: how can you proove he the proof "if both pairs of opposite angles are congruent in a quadralateral then it is a parallelogram"

Question 276923: how can you proove he the proof "if both pairs of opposite angles are congruent in a quadralateral then it is a parallelogram"
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

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