Question

In δabc, the bisector ad of is perpendicular to side bc.show that ab= ac

Answer 1

Given: In ∆ ABC, AD is the perpendicular bisector of BC.
To Prove: A ABC is an isosceles triangle in which AB = AC.
Proof: In ∆ ADB and ∆ADC,
∠ADB = ∠ADC    | Each = 90° DB = DC
| ∵ AD is the perpendicular bisector of BC
AD = AD    | Common
∴ ∆DB ≅ ∆ADC    | By SAS Rule
∴ AB = AC    | C.P.C.T.
∴ ∆ABC is an isosceles triangle in which AB = AC.