Question

Given and Proof in photo

Answer 1

We are here given that BD and AC bisect each other. Therefore ,

• BE = DE
• AE = EC

Again here , angle AEB and angle DEC are vertically opposite angles . So they will be equal.

• ang. AEB = ang. DEC

Therefore in ∆ABE and ∆CDE ,

• BE = DE ( given)
• AE = EC ( given)
• ang. AEB = ang. DEC ( v.o.a)

Therefore by SAS congruence condition ,

• ∆ABE
  `\cong` ∆CDE

Hence proved!