SOLUTION: If I knew that angle A and angle C were congruent. As well as angle B and angle D were congruent. How would I prove that ABCD is a parralelogram.

Algebra ->  Parallelograms -> SOLUTION: If I knew that angle A and angle C were congruent. As well as angle B and angle D were congruent. How would I prove that ABCD is a parralelogram.      Log On


   

Question 1003919: If I knew that angle A and angle C were congruent. As well as angle B and angle D were congruent. How would I prove that ABCD is a parralelogram.
Answer by ikleyn(53763) About Me  (Show Source):
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If I knew that angle A and angle C were congruent. As well as angle B and angle D were congruent. How would I prove that ABCD is a highlight%28parallelogram%29.
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From the condition,  you have   LA + LB = LC + LD.

In addition,  you know that the sum of internal angles of a quadrilateral is  360°.

It implies that   LA + LB = LC + LD = 180°.

In other words, the sum of two consecutive angles in your quadrilateral is 180° for any two consecutive angles.

It implies that your quadrilateral is a parallelogram.

(Because two consecutive angles are  interior angles at the same side  of two lines transversed by the third line.
Therefore,  these two lines are parallel.  See the lesson  Parallel lines  in this site).