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