3.
ABC is an isosceles triangle in which altitudes
BE and CF are drawn to equal sides AC and AB
respectively (see Fig. 7.31). Show that these
altitudes are equal.
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Given : ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC & AB respectively
To Find : Show that these altitudes are equal.
Solution:
ABC is an isosceles triangle
AB = AC
BE ⊥ AC
CF ⊥ AB
Area of Δ ABC = (1/2) * AC * BE
Area of Δ ABC = (1/2) * AB * CF
Equating area
(1/2) * AC * BE = (1/2) * AB * CF
=> AC * BE = AB * CF
AB = AC
=> BE = CF
QED
Hence Proved these altitudes are equal.
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