Question

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Prove that the angle bisectors of a parallelogram form a rectangle.



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Answer 1

To prove: MNOP is a rectangle.

In parallelogram ABCD

∠A=∠D=90

∘

[they form a straight line]

∴IN△AMD,∠M=90

∘

∠M=∠N=90

∘

[they form a straight line]

Similarly,

∠M=∠P=90

∘

And

∠P=∠O=90

∘

∴∠MPO=∠PON∠ONM=∠NMO=90

∘

∴ MNOP is a rectangle. [A rectangle is a parallelogram with one angle 90

∘

]

solution

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Answer 2

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