AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC (ii) AD bisects ∠ A.
Solution (i)
It is given that
is isosceles with AB=AC and AD is perpendicular to BC.
We need to prove that BD=CD.
In
and
, we have
(Given)
(Each given equal to
)
(Common)
Therefore, by RHS congruence rule,
Hence, we have BD=CD (Corresponding parts of congruent triangles are equal).
Solution (ii)
We have proved above that
.
It means that
(Corresponding parts of congruent triangles are equal).
means that AD bisects
.
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