Question

"Question 3 ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

Class 9 - Math - Triangles Page 124"

Answer 1

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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Hope this will help you....

Answer 2

here is your answer