Using the given figure, prove that the triangles are congruent. Can yo

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

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

Answer»

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.