If altitudes CE and BD of a triangle ABC are equal, then AB= $. . . .$

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Solution

The correct option is A AC
Given: $△ A B C$ , $B D ⊥ A C$ and $C E ⊥ A B$ , $B D = C E$
Area of triangle = $\frac{1}{2} b a s e \times h e i g h t$
Area of $△ A B C$ = $\frac{1}{2} A B \times C E = \frac{1}{2} B D \times A C$
$A B = A C$ (Since, $B D = C E$ )

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Similar questions

. . . .

Fill in the blanks in the following so that each of the following statements is true.

(i) Sides opposite to equal angles of a triangle are ___

(ii) Angle opposite to equal sides of a triangle are ___

(iii) In an equilateral triangle all angles are ___

(iv) In a $Δ A B C i f ∠ A = ∠ C, t h e n A B =$ ___

(v) If altitudes CE and BF of a triangle ABC are equal, then AB = ___

(vi) In an isosceles, triangle ABC with AB = AC, if BD and CE are its altitudes then BD is ___ CE.

(vii) In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then $Δ A B C ≅ Δ$ ___

In Fig. BD and CE are two altitudes of a $Δ$ ABC such that BD = CE.

Prove that the ABC is an isoceles triangle. [2 MARKS]

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