Question

In Fig. 7.21, AC = AE, AB = AD and ∠ BAD = ∠ EAC. Show that BC = DE.

Answer 1

It is given that EPA = DPB 

∴∠EPA +∠ DPE = ∠DPB + ∠DPE 

∴ ∠DPA = ∠EPB

 In ∆DAP and ∆EBP,

 ∠DAP = ∠EBP (Given) 

AP = BP (P is mid-point of AB) 

∠DPA = ∠EPB (From above) 

∠∆DAP ∠∆EBP (ASA congruence rule) 

∴ AD = BE (By CPCT)