Question

The altitudes AD , BE & CF of triangle ABC are equal .Show that the measure of each angle of triangle ABC is 60 degree​

Answer 1

Answer:

In right-angle triangles BCE and CBF, we have,

BC = BC (common hypotenuse);

BE = CF (given).

Hence BCF and CBF are congruent, by RHS theorem. Comparing the triangles, we get \angle B = \angle C∠B=∠C.

This implies that

AC = AB (sides opposite to equal angles).

Similarly,

AD = BE \Rightarrow \angle B = \angle AAD=BE⇒∠B=∠A

\Rightarrow AC = BC⇒AC=BC

Together, we get AB = BC = ACAB=BC=ACor \triangle ABC△ABC is equilateral. [hence \quad proved][henceproved]