Question

AB is a line segment and P is its mid - point . D andE are points on the same side of AB such that angle BAD =angle ABE and angle EPA=angle DPB.
show that:
1)∆DAP is congruent to∆EBP
2)AD=BE​

Answer 1

Answer

i)

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)

Answer 2

Answer:

sorry........................................