Question

in ABC, the bisector AD of AIs 1 of side BC. show that AB= AC& ABC is isosceles​

Answer 1

Step-by-step explanation:

Ex7.2, 2

In ABC, AD is the perpendicular bisector of BC (see the given

figure) Show that ABC is an isosceles triangle in which AB = AC

Given:

Line AD is perpendicular to BC

SO, LADC = LADB = 90

(1)

(1)

& Line AD bisects line BC

(as it is perpendicular bisector)

BD = CD

-(2)

To prove: A ABC is isosceles, i.e. AB = AC

Proof:

In AABD and AACD,

AD = AD

ZADB = ZADC

BD = CD

& ΔADC ΔADB

(Common)

(From (1)

{From (2)

(SAS congruence rule)

AB=AC CPCT)

Therefore, ABC is an isosceles triangle in which AB AC,

Hence proved