Question

ABC is a triangle in which be and CF are respectively,perpendicular to the sides AC and AC .If BE=CF,prove that∆ABC is isosceles​

Answer 1

Answer:

Step-by-step explanation:

ABC is a triangle in which BE and CF are respectively the perpendiculars to the sides AC and AB

Area of Triangle  Δ ABC  = (1/2) Base * Height

BE & CF are perpendicular so height

= (1/2) AC  * BE

or

= (1/2) AB * CF

Equating both areas

(1/2) AC  * BE  = (1/2) AB * CF

=> AC * BE = AB * CF

given BE = CF

=> AC * CF = AB * CF

=> AC = AB

=>  triangle ABC is isosceles