prove that the bisectors of two opposite angles of a parallelogram are parallel
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ABCD is a parallelogram: AD base. Now draw bisectors from B meeting CD in F and bisector from D meeting AB in E.
We have EAD =EDC = D/2 and ABF = FBC = B/2
remember B+C = 180 degress and also C+D = 180
To prove BF & ED parallel
ie., EDC = D/2 = BFC ie., ED & BF make same angle with CD.
angle BFC = 180 - C - B/2 = B - B / 2 = B/2 or D/2 as angles B = D.
= angle EDC
So proved.
We have EAD =EDC = D/2 and ABF = FBC = B/2
remember B+C = 180 degress and also C+D = 180
To prove BF & ED parallel
ie., EDC = D/2 = BFC ie., ED & BF make same angle with CD.
angle BFC = 180 - C - B/2 = B - B / 2 = B/2 or D/2 as angles B = D.
= angle EDC
So proved.
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