Question

Suppose ABC is a triangle in which BE and CF are respectively the perpendiculars to the sides AC and AB. if BE = CF, prove that triangle ABC is isosceles.

Answer 1

solve in this picture by using this method which is shown in figure

Answer 2

Answer:

triangle ABC is isosceles

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