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In ABC, A...

Question

In $△ A B C$ , $A B = A C$ ; $B E ⊥ A C$ and $C F ⊥ A B$ . Prove that : $A F = A E$ .

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Solution

In $△ A B C$ , $A B = A C$
Thus, $∠ B = ∠ C$ (I) (angles opposite to equal sides are equal)
In $△ B E C$ and $△ B F C$
$\Rightarrow ∠ E = ∠ F = 90^{o}$ ...(Given)
$\Rightarrow B C = B C$ ...(common side)
$\Rightarrow ∠ A B C = ∠ A C B$ ...(From I)
Thus, $△ B E C ≅ △ B F C$ ....(SAA test of Congruency)
Hence, $B F = C E$
Given, $A B = A C$
$\Rightarrow A B - B F = A C - C E$
$\Rightarrow A F = A E$

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Similar questions

In triangle ABC, AB = AC; BE $⊥$ AC and CF $⊥$ AB. Prove that :

(i) BE =CF

(ii) AF = AE

A B = A C

B E

⊥

A C

C F

⊥

A B

A F = A E

△ A B C

A B = A C

B E ⊥ A C

C F ⊥ A B

B E = C F

A B = C F, E F = B D

A F E = ∠ C B D

△ A F E = △ C B D

A E = C D

A B = A C

A F > A E

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