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Proofs : Quadrilaterals

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1- Prove that in a cyclic quadrilateral we have opposite angles supplementary without introducing the center of the circle.

2- Prove that a quadrilateral is paralleogram if it is simple and opposite angles are congurent.

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Quadrilateral proofs are provided. The solution is detailed and well presented. Diagrams are included.

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1- prove that in a cyclic quadrilateral we have opposite angles supplementary without introducing the center of the circle.
Solution:

Consider a cyclic quadrilateral ABCD
Draw AC and BD.
Now, ...

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