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In the given figure, $B E ⊥ C A$ and $C F ⊥ B A$ such that $B E = C F$ . Then, which of the following is true?

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Δ A B C ≅ Δ A C F

Δ A B E ≅ Δ C A F

Δ A B E ≅ Δ A C F

Δ A B C ≅ Δ A F C

answer is C.

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Detailed Solution

It is given that

B E ⊥ C A

and

C F ⊥ B A

.
And

B E = C F

.
Evaluate all the conditions.
In

Δ A B E

and

Δ A C F

∠ A

is the common angle.

B E = C F

∠ A = ∠ A

∠ B E A = ∠ C F A

.
Hence, by AAS test

Δ A B E ≅ Δ A C F

.
Hence option 3) is correct.

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