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)