Question

abc is an isoceles triangle in which the altitudes BE. and CF are drawn to the sides AC and AB respectively.Show that these altitudes are equal​

Answer 1

ΔABC is an isosceles triangle.

∴ AB = AC

⇒ ∠ACB = ∠ABC

[∴ Angles opposite to equal sides are equal]

Now, in ΔBEC and ΔCFB, we have

∠EBC = ∠FCB

[Proved]

BC = CB

[Common]

and ∠BEC = ∠CFB

[Each = 90°]

∴ ΔBEC ≌ ΔCFB

[Using ASA criteria]

⇒ Their corresponding parts are equal.

i.e. BE = CF