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Question

Prove that the bisectors of the interior angles of a rectangle form a rectangle.

Solution
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1=902=45o

Similarly, 2=902=45o

In AXD,

=1804545=90o

WXY=90o [vertically opposite angles]

Similarly in BCZ,

CZB=WZY=90o

Since all the angles will be 90o and hence it will be a rectangle.

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