Question

ABC is an isosceles triangle in which attitudes be and CF are drawn to equal sides AC and ab respectively show that these attitudes are equal.
​

Answer 1

SOLUTION:-

Given:-

• ABC is an isocless ∆.
• BE perpendicular AC
• CF perpendicular AB

Need to prove:-

• BE = CF

PROOF:-

In ∆AEB and ∆AFC

=> <AEB = <AFC = 90° [Given]

=> <A = <A [common]

=> AC = AB [Given]

Therefore,

∆ AEB congruent to ∆ AFC [By AAS congruence]

Therefore,

BE = CF [BY CPCT]

Hence proved✔️

Answer 2

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.