Question

8. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that
ZBAD ZABE and ZEPA - / DPB (figure given below). Show that (i) ADAP=AEBP
(ii) AD = BЕ.
HP Ep
Pris
ДА В
P3
PA
gine
인
- В
Р
B В
P Р
OPE
- Хор​

Answer 1

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)