Question

AB is line segment and P is the mid point .D and E are point on the same side of AB such that angle BAD=angle ABE and angleEPA=angleDPB
Show that
(I) ∆Dap congruent to ∆EBP
(ii)AD=BD​

Answer 1

Answer:

Step-by-step explanation:

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)