Question

AB is a line segment and P is its mid-point. D and E are points on the
same side of AB such that BAE= ABD and 2 DPA = EPB. (see
figure). Show that
(0)EAP=
DBP

Answer 1

Answer:

EPA=∠DPB (Given)

∠EPA+∠DPE=∠DPB+∠DPE

∠APD=∠BPE........... (1)

Now, in △DAP and △EBP,

AP=PB, (∵P is the mid point of AB)

∠PAD=∠PBE (Given)

∠APD=∠BPE (By 1)

△DAP≅△EPB (ASA rule)

Thus, AD=BE (By CPCT)