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



Show that


(i) ΔDAP ≅ ΔEBP

(ii) AD = BE

Answer 1

As ∠ EPA = ∠ DPB (Given)

⇒ ∠ EPA + ∠DPE = ∠ DPB + ∠DPE

∴ ∠APD = ∠BPE …(i)

Now in ΔDAP and ΔEBP

AP = BP (Given P is midpoint of AB)

∠BAD = ∠ABE (Given)

∠APD = ∠BPE (From equation (i))

Hence ΔDAP ≅ ΔEBP (By ASA congruence rule)

⇒ AD = BE (CPCT)

Answer 2

Hey mate

Here's the answer

Hope it helps