Question

Short Proofs - No Triangle Congruence

Answer 1

Step-by-step explanation:

Given,

∠CBE ≅ ∠DBE ----> 1

∠CBE ≅ ∠BCA ----> 2

From 1 & 2,

∠BCA≅ ∠DBE ----> 3

∠DBE ≅ ∠BAC ----> 4

Reason,

Since BE II AC, corresponding angles are equal.

From 3 & 4,

∠BCA ≅ ∠BAC

BC is opposite to ∠BCA

AB is opposite to ∠ABC

Side opposite to congruent angles are always congruent.

Therefore,

AB ≅ BC

Hence proved.