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In two triangle ABC and DEF, AB= DE ,BC=...

In two triangle ABC and DEF, AB= DE ,BC=DF and AC =Ef then

A

`/_\ABC~=/_\DEF`

B

`/_\ABC~=/_\FED`

C

`/_\ABC~=/_\ESE`

D

None of these

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the given information about triangles ABC and DEF. ### Step-by-Step Solution: 1. **Identify the Given Information:** We have two triangles, ABC and DEF. The sides are given as: - AB = DE - BC = DF - AC = EF 2. **Apply the SSS Congruence Criterion:** The SSS (Side-Side-Side) congruence criterion states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent. 3. **Check the Conditions:** Since we have: - AB = DE - BC = DF - AC = EF All three pairs of corresponding sides are equal. 4. **Conclude the Congruence:** According to the SSS criterion, since all three sides of triangle ABC are equal to the corresponding sides of triangle DEF, we can conclude that: - Triangle ABC is congruent to triangle DEF. 5. **Identify the Options:** The question may provide multiple-choice options. Based on the conclusion that triangles ABC and DEF are congruent, we can analyze the options provided. 6. **Determine the Correct Option:** If one of the options states that triangle ABC is congruent to triangle DEF, that would be the correct answer. If there is an option stating that there is no triangle DEF, that would also be correct based on the context provided in the video transcript. ### Final Conclusion: Triangle ABC is congruent to triangle DEF by the SSS criterion. ---
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