1.

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 the given figure). Show that (i) ΔDAP ≅ ΔEBP(ii) AD = BE

Answer»

It is given that EPA = DPB

EPA + DPE = DPB + DPE

DPA = EPB

In ΔDAP and ΔEBP,

DAP = EBP (Given)

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

DPA = EPB (From above)

∴ ΔDAP  ΔEBP (ASA congruence rule)

AD = BE (By CPCT)



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