How do the angle bisectors of the internal angles of a parallelogram form a rectangle?

Expert Solution

let angles of parallelogram be alpha, beta, alpha, beta

2 alpha + 2 beta = 360 degrees

==> alpha + beta = 180

in triangle formed by angle bisectors,

alpha / 2 + beta / 2 + gamma = 180

==> gamma = 90 degrees

so angle bisectors form a right angle triangle

Since adjacent angles of the parallelogram are supplementary, the angle bisectors will meet each other at 90 degrees. So you have a quadrilateral with all four angles 90 deg each, so the quadrilateral is a rectangle.

Given below:

Nipun Maity answered 2 years ago

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