
Prove Triangle Is Isosceles using Coordinate Geometry
An isosceles triangle has 2 congruent sides and two congruent angles. The easiest way to prove that a triangle is isosceles using coordinate geometry is to use the sides.
Steps to Coordinate Proof
Given the coordinates of the triangle's vertices, to prove that a triangle is isosceles
Practice Problem 2) Triangle ABC has coordinate A(2,3) , B (5,4) and C (2,1) Using coordinate geometry, prove that triangle BCD is an isosceles triangle.
Calculate all 3 distances
The distances
If you calculated side lengths AB and BC first, you could stopthe triangle must be isosceles at this point since you found 2 sides that are congruent. (Granted, the triangle still could be equilateral)
Step 4) Draw your conclusion 
Triangle ABC is isosceles because 2 of the sides have equal side length (ie are congruent)
