Question

in triangle ABC, AD is perpendicular bisects of BC. show that triangle ABC is an isosceles triangle in which AB=AC​

Answer 1

Since, AD is a perpendicular bisector of BC

We get BD = DC and ∠ADB = ADC = 90°

Now,

In triangle ADB and ADC,

AD = AD (common)

∠ADB = ADC = 90° (given)

BD = DC (given)

(SAS congruency)

Thus, AB = AC (corresponding parts of congruent triangles)

Hence, triangle ABC is an isosceles triangle.

Answer 2

Step-by-step explanation:

Given : ΔABC and AD is perpendicular to BC and it bisects BC(that is BD=DC)

To Prove: AB = AC

PROOF IN ΔABC

AD = AD (COMMON)

∠ADB=  ∠ADC ( 90 )(PERPENDICULAR)

BD = CD ( GIVEN ABOVE)

THEREFORE THE TRIANGLE IS CONGRUENT BY SAS  RULE

AB = AC (CPCT) CORRESPONDING PARTS OF CONGRUENT TRIANGLE

HENCE PROVED