Question

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Answer 1

Solution:

Given ..................

To prove : ΔBAP ≅ ΔCAP

               : BP =CP

Proof :

           ∠APC + ∠CPD = 180 (Linear pair)

                         ∠CPD = 180 - ∠APC                .......(i)

           ∠APB + ∠BPD = 180 (Linear pair)

                        ∠BPD = 180 - ∠APB                 .......(ii)

           Since ∠CPD = ∠BPD (Given)               .......(iii)

   From i , ii and iii

   ∠APC = ∠APB

Now ∠ACP = ∠ABP ( They both are the part of Triangles whose 2 other angles are equal hence by Angle Sum property they are also equal )

                In Δ BAP and Δ CAP

                ∠BAP = ∠CAP ( They are bisected )

                ∠APB = ∠APC ( proved above )

                ∠ABP = ∠ACP ( proved above )

          ∴ ΔBAP ≅ ΔCAP ( AAA congruence rule)

    and

              BP = CP ( CPCT)

                                                                   Hence Proved !