The Total solution for NCERT class 6-12
ABC is a triangle in which altitudes BE and CF to sides ACand AB are equal (see the given figure). Show that
(i) ABE ≅ ACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.
(i) In ΔABE and ΔACF,
∠AEB = ∠AFC (Each90º)
∠A = ∠A (Common angle)
BE = CF (Given)
∴ ΔABE ≅ ΔACF (By AAS congruence rule)
(ii) It has already been proved that
ΔABE ≅ ΔACF