Question

given figure 1:2 and AB=AC Prove that B:C BD=DC and AD is perpendicular to BC ​

Answer 1

Answer:

In ΔADB and ΔADC

It is given that

AB=AC

and ∠1=∠2

AD=AD is common

Hence , ΔADB≅ΔADC (SAS Axiom)

(i) ∠B=∠C (c.p.c.t)

(ii) BD=DC (c.p.c.t)

(iii) ∠ADB=∠ADC (c.p.c.t)

We know that

∠ADB+∠ADC=180° is a linear pair

So we get

∠ADB=∠ADC=90°

AD is perpendicular to BC

Therefore , it is proved