Math, asked by vinayak829351ab, 1 year ago

in the following figure ABCD is a parallelogram prove that AP bisects angle A B P bisects Angle B angle d a p + angle cbp equals to angle APB​

Answers

Answered by amitnrw
17

∠APB = ∠DAP + ∠CBP  if ABCD is a parallelogram and AP & BP bisects ∠A & ∠B

Step-by-step explanation:

in a parallelogram

sum of adjacent angles = 180°

=> ∠A + ∠B = 180°

AP bisects ∠A

=>  ∠BAP  = ∠A -  ∠DAP

BP bisects ∠B

=>  ∠ABP  = ∠B - ∠CBP

in Δ ABP

∠BAP + ∠ABP  + ∠APB  = 180°

∠A -  ∠DAP + ∠B - ∠CBP + ∠APB  = 180°

=> ( ∠A +  ∠B) + ∠APB = 180°   + ∠DAP + ∠CBP

=> 180° + ∠APB = 180°   + ∠DAP + ∠CBP

=> ∠APB = ∠DAP + ∠CBP

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