Question

Using the given figure, prove that the triangles are congruent. Can you conclude that AC is parallel to DE

Answer 1

In ∆ABC and ∆EBD,
AB = EB

BC = BD

∠ABC = ∠EBD   ...[∵ Vertically opposite angles]

By SAS congruency criteria ∆ABC ≅ ∆EBD.

We know that corresponding parts of congruent triangles are congruent.

∴ ∠BCA ≅ ∠BDE and ∠BAC ≅ ∠BED

∠BCA ≅ ∠BDE means that alternate interior angles are equal if CD is the transversal to lines AC and DE.

Similarly, if AE is the transversal to AC and DE,

we have ∠BAC ≅ ∠BED

Again interior opposite angles are equal.

We can conclude that AC is parallel to DE.