Question 4:
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the
given figure). Show that
(i) ∆ABE ≅ ∆ACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.
Answer:
(i) In ∆ABE and ∆ACF,
∠ABE and ∠ACF (Each 90º)
∠A = ∠A (Common angle)
BE = CF (Given)
∆ABE ≅ ∆ACF (By AAS congruence rule)
(ii) It has already been proved that
∆ABE ≅ ∆ACF
AB = AC (By CPCT)
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