AB = AC

           [Angles opposite to equal sides of isosceles ]

                       [ CE and BD are the bisectors of and , respectively]

BP = PC                     .....(i)   [Side oppoite to equal angles of ]

In BPE and CPD,

      BP = CP                             [proved above]

          [Proved above]

          [Vertically opposite angles]

       [ASA axiom]

       PE = PD                        [CPCT]

     PD = PE                     ....(iii)

Adding (i) and (ii), we get

    BP + PD = PC + PE                     BD = CE

Draw the angle

and no. 10

page no. 3