Question

ABC is a triangle in which altitudes BD and CE to sides AC and AB are equal (see figure). Show that 

i) ΔABD ≅ ΔACE 

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

Answer 1

Given that BD ⊥ AC; CE ⊥ AC 

BD = CE 

Now in ΔABD and ΔACE 

∠ADB = ∠AEC (∵ given 90°) 

∠A = ∠A (commori angle)

BD = CE 

∴ ΔABD = ΔACE (∵ AAS congruence)

⇒ AB = AC (∵ C.P.C.T)