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Sum of co-interior angles between parall...

Sum of co-interior angles between parallel lines is two right angles

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A B ,C D are two parallel lines and a transversal l intersects A B at X and C D at Y Prove that the bisectors of the interior angles form a parallelogram, with all its angles right angles i.e., it is a rectangle.

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A transverals cuts two parallel lines at A and B. The two interior angles at A are bisected and so are the two interior angles at B, the four bisectors from a quadrilateral ACBD, prove that ABCD is parallelogram.