In an isosceles triangle ABC, with AB=AC, the bisectors of
and
intersect each other at O. Join A to O. Show that:
(i)
(ii) AO bisects
Solution (i)
It is given that AB=AC
Therefore,
(Angles opposite to equal sides are equal)
(OB and OC are bisectors of
and
)
Therefore, OB=OC (Sides opposite to equal angles are equal)
Solution (ii)
In
and
OB=OC (Proved above)
(Angles opposite to equal sides are equal)
(OB and OC are bisectors of
and
)
AB=AC (Given)
Therefore, by SAS rule,
So,
(Corresponding parts of congruent triangles are equal)
It means that AO bisects
.
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