Z AB is a line segment and P is its mid-point. D andE are points on th

1.	Z AB is a line segment and P is its mid-point. D andE are points on the same side of AB such thatBAD = < ABE and EPA-L DPB(see Fig. 7.22). Show that(ii) AD BE
Answer» EPA = ∠ DPB (Given) ⇒ ∠ EPA + ∠DPE = ∠ DPB + ∠DPE ∴ ∠APD = ∠BPE Consider Δ’s DAP and EBP AP = BP (Given P is midpoint of AB) ∠BAD = ∠ABE (Given) ∠APD = ∠BPE (Proved) Hence ΔDAP ≅ ΔEBP (By ASA congruence rule) ⇒ AD = BE (CPCT)

Z AB is a line segment and P is its mid-point. D andE are points on the same side of AB such thatBAD = < ABE and EPA-L DPB(see Fig. 7.22). Show that(ii) AD BE

Answer»

EPA = ∠ DPB (Given)

⇒ ∠ EPA + ∠DPE = ∠ DPB + ∠DPE

∴ ∠APD = ∠BPE

Consider Δ’s DAP and EBP

AP = BP (Given P is midpoint of AB)

∠BAD = ∠ABE (Given)

∠APD = ∠BPE (Proved)

Hence ΔDAP ≅ ΔEBP (By ASA congruence rule)

⇒ AD = BE (CPCT)