Question

4.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 = LABE and LEPA = ZDPB.Show that : ADAP AEBP and AD = BE​

Answer 1

Answer:

Given:

P is the mid point of AB,

So,AP=BP .....(1)

∠BAD= ∠ABE .....(2)

∠EPA = ∠ DPB .....(3)

To prove:

(I) △DAP ≅ △EBP

(ii) AD=BE

Proof: Since

∠EPA = ∠DPB

We add ∠DPE both sides

∠EPA + ∠DPE = ∠DPB + ∠DPE

∠DPA = ∠EPB .....(4)

In △DAP and △EBP,

∠DAP = ∠EBP .....[From(2)]

AP = BP .....[From(1)]

∠DPA = ∠EPB.....[From(4)]

∴ △ DPA ≅ △EBP.....(ASA congruence rule)

∴AD = BE .....(C.P.C.T.)

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