Question

In Fig. 7.21, AC = AE, AB = AD and
BAD=2 EAC. Show that BC=DE.
A
B
D C
Fig. 7.21​

Answer 1

Answer:

 It is given that ∠BAD=∠EAC

∠BAD+∠DAC=∠EAC+∠DAC   [add ∠DAC on both sides]

∴∠BAC=∠DAE

In △BAC and △DAE

AB=AD (Given)

∠BAC=∠DAE (Proved above)

AC=AE (Given)

∴△BAC≅△DAE (By SAS congruence rule)

∴BC=DE (By CPCT)