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.
Solution:
In
and
, we have
(Angles opposite to equal sides are equal, AB=AC)
(Each given equal to
)
BC=CB (Common)
Therefore, by AAS rule,
Hence, CF=BE (Corresponding parts of congruent triangles are equal)
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