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

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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) About Me  (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