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