Question

ABC is an isosceless triangle in which altitudes
BE and CF are drawn to equal sides AC and AB
respectively (see Fig. 6.31). Show that these
altitudes are equal.​

Answer 1

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Answer 2

Congruence of triangles:

Two ∆’s are congruent if sides and angles of a triangle are equal to the corresponding sides and angles of the other ∆.

In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.

It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.

Criteria for congruence of triangles:

There are 4 criteria for congruence of triangles.

Here we use ASA congruence

ASA(angle side angle):

Two Triangles are congruent if two angles and the included side of One triangle are equal to two angles & the included side of the other triangle.

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Given:

ΔABC is an isosceles∆ with AB = AC, BE and CF are altitudes.

To prove:

BE = CF

Proof:

In ΔAEB and ΔAFC,

∠A = ∠A (Common)

∠AEB = ∠AFC (each 90°)

AB = AC (Given)

Therefore, ΔAEB ≅ ΔAFC

(by AAS congruence rule)

Thus, BE = CF (by CPCT.)

Hence , altitudes BE & CF are equal.

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