Question

please answer this questions as soon as possible

Answer 1

Given: 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.
To Prove: (i) ∆DAP ≅ ∆EBP
(ii) AD = BE.
Proof: (i) In ∆DAP and ∆EBP,
AP = BP
| ∵ P is the mid-point of the line segment AB
∠DAP = ∠EBP | Given
∠EPA = ∠DPB | Given
⇒ ∠EPA + ∠EPD = ∠EPD + ∠DPB
| Adding ∠EPD to both sides
⇒ ∠APD = ∠BPE
∴ ∠DAP ≅ ∠EBP | ASA Rule
(ii) ∵ ∆DAP ≅ AEBP | From (i) above
∴ AD = BE. | C.P.C.T.

Answer 2

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