Question

In the given figure, BE and CE are the bisectors of the angles B and C respectively of ∆ABC. If EF⊥BC and

CD⊥AB, then prove that

(i) ∆BED ≅ ∆BEF

(ii) AE bisects ∠A​

Answer 1

Step-by-step explanation:

i ) Given: BE bisects angle B, so ∠EBF= ∠EBD

,CE bisects angle C, so ∠ECF= ∠ECA

,EF⊥BC

, CD⊥AB

Proven: In ∆BEF and ∆BED

1. ∠EBF=∠EBD (as BE bisects angle B)
2. ∠BDE=∠BFE=90° (given)
3. BE is common side in both the triangles.

Hence, ∆BED ≅ ∆BEF(proved)

ii) In ∆ABF and ∆AFC

BF=CF ( as EF⊥BC)

Therefore their opposite angles should also equal.

=» ∠BAE= ∠CAE

hence proved that AE bisects ∠A.