In ∆ ABC, two points D and E are taken on the lines

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In ∆ ABC, two points D and E are taken on the lines AB and BC respectively in such a way that AC is parallel to DE. Then ∆ ABC and ∆ DBE are

1. similar only if D lies outside the line segment AB
2. congruent only if D lies outside the line segment AB
3. always similar
4. always congruent

Correct Option: C

According to question , we draw a figure triangle ABC in which two points D and E are taken on the lines AB and BC respectively in such a way that AC is parallel to DE ,

In ∆ ABC and ∆ DBE,
DE || AC
∴ ∠BAC = ∠BDE
∠BCA = ∠BED
∴ By AA–similarity
∆ ABC ~ ∆ DBE
From above it is clear that ∆ ABC and ∆ DBE are congruent triangles .