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प्रश्न
Using the given figure, prove that the triangles are congruent. Can you conclude that AC is parallel to DE
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उत्तर
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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संबंधित प्रश्न
Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by using the SAS congruence rule. If the triangles are congruent, write them in symbolic form.
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