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12/07/2021 11:24 am
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ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Figure). Show that
(i) ΔABE ΔACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.
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12/07/2021 11:26 am
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.