ABCD is a quadrilateral.
AB = CD.
Angle DAB = angle CDA.
Prove that AC = BD.
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Answer:
Draw the diagonals AC and BD, and observe the two triangles ABD and ACD you created. They have side lenghths AB and CD equal by hypotesis, side lenght AD in common, and the angle inbetween congruent by hypotesis. The two triangles are congruent (albeit mirrored vertically) by SAS. The third sides are then congruent, QED.