ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.

Question

Philoid · Accepted Answer

It is given in the question that:

BE and CF are altitudes

AC = AB

To show: BE = CF

Proof: In

∠A = ∠A (Common)

∠AEB = ∠AFC (Right angles)

AB = AC (Given)

Therefore,

By AAS congruence axiom,

Thus,

BE = CF (By corresponding parts of congruent triangles)