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 (see Fig). Show that

(i) ∆ DAP ≅ ∆ EBP

(ii) AD = BE

Answer 1

It is given that EPA = DPB

∠EPA +∠ DPE = ∠DPB + ∠DPE

∠DPA = ∠EPB

In ∆DAP and ∆EBP,

∠DAP = ∠EBP (Given)

AP = BP (P is mid-point of AB)

∠DPA = ∠EPB (From above)

∠∆DAP ∠∆EBP (ASA congruence rule)

∴ AD = BE (By CPCT)