Question

Prove that in an equilateral triangle the perpendicular bisector

Is also a angle bisector. (Same figure given above​

Answer 1

Answer:

In the above triangle, let us consider AD to be the median.

and △ABC to be an equilateral triangle.

By definition of equilateral triangle, AB=BC=AC .

Step-by-step explanation:

In △ACD and △ABD ,

CD=BD (median divides BC into two equal halves)

AD = AD (common to both sides)

AC=AB (By definition of equilateral triangle)

By SSS axiom of congruency, △ACD≅△ABD .

∠ACD=∠ABD (Corresponding part of congruent triangles are congruent)

And hence we've proved that median is the angle bisector as well (in case of equilateral triangle).