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
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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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