Question

Ab is a line segment and p is its midpoint.d and e are the same points of the same side of AB such that angle BAD equal angle ABE and angle EPA equal angle DPB in the figure.show that AB equals DE

Answer 1

It is given that ∠EPA=∠DPB

➜Now,

➙∠EPA+∠DPE=∠DPB+∠DPE

____Therefore, ______

➜∠DPA=∠EPB

➜In ΔEBP and ΔDAP,

➜∠EBP=∠DAP (given)

➜BP=AP (P is midpoint of AB)

➙∠EPB=∠DPA [proved above]

⇺By ASA criterion of congruence,

➙ΔEBP≅ΔDAP

➙ii) Since ΔEBP≅ΔDAP

➥AD=BE (using CPCT)