4. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
Solution: It is known that BE and CF are two equal altitudes. Now, in ΔBEC and ΔCFB, ∠BEC = ∠CFB = 90° (Same Altitudes) BC = CB (Common side) BE = CF (Common side) So, ΔBEC ≅ ΔCFB by RHS congruence criterion. Also, ∠C = ∠B (by CPCT) Therefore, AB = AC as sides opposite to the equal angles is always equal.
