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Mathematics

If ΔABC and ΔDEF are so related that ABFD=BCDE=CAEF\dfrac{AB}{FD} = \dfrac{BC}{DE} = \dfrac{CA}{EF}, then which of the following is true?

  1. ∠A = ∠E and ∠B = ∠D

  2. ∠B = ∠F and ∠C = ∠D

  3. ∠A = ∠F and ∠B = ∠D

  4. ∠C = ∠F and ∠A = ∠D

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Answer

Given,

ABFD=BCDE=CAEF\dfrac{AB}{FD} = \dfrac{BC}{DE} = \dfrac{CA}{EF}

∴ ΔABC ∼ ΔDEF BY SSS theorem.

Side AB corresponds to side FD. Therefore, vertex A corresponds to vertex F and vertex B corresponds to vertex D.

Side BC corresponds to side DE. Therefore, vertex B corresponding to D. It also implies vertex C corresponds to vertex E. 

Since the triangles are similar, the corresponding angles are also similar,

∠A = ∠F and ∠B = ∠D

Hence, option 3 is the correct option.

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