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.
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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) (Show Source): You can put this solution on YOUR website!
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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 .
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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).
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