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