4. ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that (i) ΔABE ≅ ΔACF (ii) AB = AC, i.e., ABC is an isosceles triangle.
Solution: It is given that BE = CF (i) In ΔABE and ΔACF, ∠A = ∠A (It is the common angle) ∠AEB = ∠AFC (They are right angles) BE = CF (Given in the question) ∴ ΔABE ≅ ΔACF by AAS congruency condition. (ii) AB = AC by CPCT and so, ABC is an isosceles triangle.
