in a parallelogram show that angle bisectors two adjacent angles intersect at right angles
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Draw a parallelogram ABCD.
let the adjacent angles taken be < A and <B.
<A + <B = 180 ( co-interior angles)
AP and BP bisects <A and <B Dr respectively.
<PAB + <PBA = 180รท 2
<PAB+< PBA=90 ------ (1)
In triangle PAB,
<PBA+<PAB+<APB=180 (angle sum property)
90+<APB=180
<APB=180-90
<APB =90
hence proved
let the adjacent angles taken be < A and <B.
<A + <B = 180 ( co-interior angles)
AP and BP bisects <A and <B Dr respectively.
<PAB + <PBA = 180รท 2
<PAB+< PBA=90 ------ (1)
In triangle PAB,
<PBA+<PAB+<APB=180 (angle sum property)
90+<APB=180
<APB=180-90
<APB =90
hence proved
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