Question

In ABC ; AD is the perpendiculas bisecter
of BC Show that ABC is an
issosceles triangle in which
AB=AC.

Answer 1

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Answer 2

Given that

In ∆ABC, AD is the perpendicular bisector of BC.  To Prove:  ∆ABC is an isosceles triangle in which AB = AC.

Proof:  I

In ∆ABC, 

AD is the perpendicular bisector of BC.

∴ BD = DC  ∴ ∠ADB = ∠ADC = 90°. 

Now, in ∆ADB and ∆ADC, 

BD = DC  (AD is the perpendicular bisector)  ∠ADB = ∠ADC = 90° (Data) 

AD is common 

∴ ∆ADB ≅ ∆ADC 

=> AB = AC

 Hence, ∆ABC is an isosceles triangle.