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 ∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB . Show that ∆ DAP ≅ ∆ EBP​

Answer 1

$\purple{Answer}$

Given:

• P is mid-point of AB
• ∠ BAD = ∠ ABE
• ∠ EPA = ∠ DPB

To prove:

• ∆ DAP ≅ ∆ EBP

Sol :

∠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