Question

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig). Show that 

(i) ∆ ABE ≅ ∆ ACF 

(ii) AB = AC, i.e., ABC is an isosceles triangle.

Answer 1

(i) In ∆ABE and ∆ACF, 

∠ABE and ∠ACF (Each 90º) 

∠A = ∠A (Common angle) 

BE = CF (Given) 

∠∆ABE  ∠∆ACF (By AAS congruence rule) 

(ii) It has already been proved that 

∠∆ABE  ∠∆ACF 

∴ AB = AC (By CPCT)