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SSS Rule

In triangle A...

Question

In triangle ABC, $A B = A C$ ; $B E$ $⊥$ $A C$ and $C F$ $⊥$ $A B$ .
State whether following statement is true or false
$A F = A E$

True

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False

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Solution

The correct option is A True
In $△ B F C$ and $△ B E C$ ,
$B C = B C$ (Common)
$∠ F C B = ∠ E B C$ (Given, AB = AC)
$∠ B F C = ∠ B E C$ (each $90^{\circ}$ )
Thus, $△ B F C ≅ △ C E B$ (ASA rule)
Hence, $B F = C E$ (By cpct)
$A B = A C$ (Given)
Hence, $A B - B F = A C - C E$
$A F = A E$

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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 C

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 = A C

B D ⊥ A C

C F ⊥ A B

B A = C F

\frac{A B}{A D} = \frac{A C}{A E}

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