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Q.

State true or false.
BE and CF are two equal altitudes of a triangle ABC. Using congruence rule, we can prove that the triangle ABC is not isosceles.

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a

True

b

False

answer is B.

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Detailed Solution

It is given a statement BE and CF are two equal altitudes of a triangle ABC. Using congruence rule, we can prove that the triangle ABC is not isosceles.
A pair of triangles can be called congruent if their corresponding sides and angles are equal.
The congruence rule states that when two right angled triangles are being compared for congruency, if the hypotenuse and one other side of a triangle is equal to the hypotenuse and side of the other triangle, the two triangles are said to be congruent.
Question Image

Question Image

Consider the triangles

∆ BFC and ∆ CEB

,
BC = BC

∠ BFC = ∠ CEB

(∵altitudes make 90°)
FC=BE (∵given in the question)
Hence,

∆ BFC ≅ ∆ CEB

Since corresponding angles of congruent triangles are equal,

∠ CBF = ∠ BCE

Sides opposite to equal angles are also equal so the triangle ABC is isosceles.
Therefore, the given statement is false.
Hence option (2) is correct.

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