Tangential Quadrilateral Converse

This sketch shows a quadrilateral that has been constructed so that its two sums of opposite sides are equal, i.e. a + b = c + d as shown.
1) Click on the Show Bisectors to show its angle bisectors. What do you notice about them?
2) Check you observation in 1) by clicking the Show Incircle button.
3) Change the shape of the quadrilateral by dragging X or Y, and repeat the above.
4) Formulate a conjecture.

Tangential Quadrilateral Converse

Challenge
1) Can you explain why (prove that) your conjecture above is true?
2) Hint: Try using proof by contradiction.

To explore some more properties of this type of quadrilateral go to: Tangential Quadrilateral

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Created by Michael de Villiers, 1 Sept 2020 with WebSketchpad.