Question

AD is is perpendicular on base BC of an isosceles triangle ABC in which AB = AC. Show that
(i) Line segment AD bisects BC
(ii) AD bisects angle A

Answer 1

GIVEN
AC=AB because it is a isoceles triangle

<C=<B becaus it is isoceles triangle

In triangle ADB AND ADC

AB=AC (GIVEN)
<ADB=<ADC (90°)
AD=AD. (COMMON)

SO BY AAS CONGRUENCE RULE
ADB=~ADC

BD=CD {CPCT}
SO AD BISECTS BC

<BAD=<CAD [CPCT]
SO AD BISECTS <A

Answer 2

This is 2 question of ex 7.3 from maths 9th NCERT Textbook
In ∆ ADC & ∆ ADB
angle ADC=angle ADB (given perpendicular)
angleACD=angleABD (isosceles∆)
AB=AC(given)
: . ∆ ADC congruent to ∆ADB
by CPCT CD=DB
angle CAD=angle DAB