Question

Prove that the bisecter of the angles of a linear pair are at right angles

Answer 1

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To prove:  Angle A/2 + angle B/2 = 90 degree

 

Linear pair of angles are supplementary.

Therefore,  ∟A + ∟B = 180 0   

∟A =  A/2  +  A/2  [ bisecting linear pairs]

∟ A  + ∟ B = 180 0

∟A/2 + ∟A/2  + ∟B/2  + ∟B/2  = 180 0

2 ∟A/2 + 2 ∟B/2 = 180 0

2 [ ∟A/2 + ∟B/2 ] = 180 0

∟A/2 + ∟B/2 = 180/2

 ∟A/2 + ∟B/2 = 90 0   

Answer 2

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