ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Figure). Show that
(i)
(ii) AB = AC, i.e, ABC is an isosceles triangle.
Solution (i)
Now in
and
, we have
(Common)
(Given)
(Each equal to
)
Therefore, by AAS rule,
Solution (ii)
We have proved above that
.
Therefore,
(Corresponding parts of congruent triangles are equal)
It means that
is isosceles.
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