Question

state mid-point theorm and find answer for the question

Answer 1

Given :   AD is the bisector of  ∠BAC

∠CPD =  ∠BPD

To Find : Prove that ΔCAP ≅ ΔBAP

Solution:

 AD is the bisector of  ∠BAC

=> ∠CAP = ∠BAP

∠APC + ∠CPD = 180°   linear pair

∠APB + ∠BPD = 180°    linear pair

=> ∠APC + ∠CPD  = ∠APB + ∠BPD

∠CPD =  ∠BPD

=>  ∠APC   = ∠APB

in ΔCAP and  ΔBAP

∠CAP = ∠BAP

AP = AP   common

∠APC   = ∠APB

=> ΔCAP ≅ ΔBAP  ( ASA)

QED  hence proved

mid-point theorem :

line joining the mid-point of two sides of a triangle is equal to half the length of the third side and parallel

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