Question

Prove that the angle bisector of a parallelogram form a rectangle .​

Answer 1

Step-by-step explanation:

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

∘

]

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Answer 2

Answer:

LMNO is a parallelogram in which bisectors of the angles L, M, N, and O intersect at P, Q, R and S to form the quadrilateral PQRS. Hence the angle bisectors of a parallelogram form a rectangle as all the angles are right angles; we conclude that it IS RECTANGLE.

Hence proved #