I'll state the theorem and use Figure 16.3 to guide you through your proof.įigure 16.3 Quadrilateral ABCD with ∠A ~= ∠C and ∠B ~= ∠D. The third description of the quadrilateral involved both pairs of opposite angles being congruent. Once again, the sweet taste of victory! You have named that quadrilateral correctly. ¯BC and ¯AD are two segments cut by a transversal ¯AC Quadrilateral ABCD with ¯AB ~= ¯CD and ¯BC ~= ¯AD It's time to write out the details.įigure 16.2 Quadrilateral ABCD with ¯AB ~= ¯CD and ¯BC ~= ¯AD If we show this for both pairs of opposite sides, then we have a parallelogram by definition. Use the SSS Postulate to show that the two triangles are congruent, and use CPOCTAC to conclude that alternate interior angles are congruent and opposite sides must be parallel. The game plan is to divide the quadrilateral into two triangles using the diagonal ¯AC. We have a parallelogram ABCD with ¯AB ~= ¯CD and ¯BC ~= ¯AD.
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