SOLUTION: Given: ABCD is a parallelogram with m < A = m < D. Prove: ABCD is a rectangle

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Question 1132255: Given: ABCD is a parallelogram with m < A = m < D. Prove: ABCD is a rectangle
Answer by ikleyn(52794) About Me  (Show Source):
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        Given: ABCD is a parallelogram with m (< A) = m (< D). Prove: ABCD is a rectangle.


Solution 

In any parallelogram, the sum of the measures of two consecutive angles is equal to 180 degrees.


So, m (< A) + m(< D) = 180 degrees,    and

    m(< A) = M(< D).                   ( <<<---=== given ! )


Therefore,  m(< A) + m(< A) = 180 detrees,   or

            2m(< A) = 180 degrees, which implies  m(< A) = 90 degrees.


Thus in our parallelogram one angle is 90 degrees.

It means that EACH angle of the given parallelogram is 90 degrees, and hence the parallelogram is a rectangle.

Proved, solved and completed.