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12/07/2021 11:20 am
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ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Figure). Show that these altitudes are equal.
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12/07/2021 11:22 am
(i) BE and CF are altitudes.
(ii) AC = AB
To prove:
BE = CF
Proof:
Triangles ΔAEB and ΔAFC are similar by AAS congruency since
A = A (It is the common arm)
AEB = AFC (They are right angles)
AB = AC (Given in the question)
∴ ΔAEB ΔAFC and BE = CF (by CPCT).