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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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