The Total solution for NCERT class 6-12
AD is an altitude of an isosceles triangles ABC in whichAB = AC. Show that
(i) AD bisects BC (ii) AD bisects ∠A.
(i) In ΔBAD and ΔCAD,
∠ADB = ∠ADC (Each 90º as AD is an altitude)
AB = AC (Given)
AD = AD (Common)
∴ΔBAD ≅ ΔCAD (By RHS Congruence rule)
⇒ BD = CD (By CPCT)
Hence, AD bisects BC.
(ii) Also, by CPCT,
∠BAD = ∠CAD