prove:if two consecutive angles of a trapezoid are cogruent, but not supplementary, the trapezoid is isosceles

Question

please prove this one...tnx

Answer 1

Let ABCD be the trapezium, with AB || CD
Drop perpendiculars from A to AC and B to CD to meet CD at E and F respy.
Consider, triangles ACE and BDF.
angle CAE = angle DBF ( subtracting 90 degrees from two equal angles)
the height is the same at both places since AB || CD.
Thus AE = BF. Also angle AEC = angle BFD = 90.
Thus by ASA, both triangles are congruent.
Consequently, AC = BD

Answer 2

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