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# 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
##### Problem 1
The coordinates of triangle BCD are B(8,2), C(11,13) and D(2,6). Using coordinate geometry, prove that triangle BCD is an isosceles triangle.
Plot points
Calculate all 3 distances
Triangle BCD is isosceles because 2 of the sides have equal side length $$\sqrt{130}$$ (ie are congruent)
Triangle ABC is isosceles because 2 of the sides have equal side length $$\sqrt{58}$$ (ie are congruent)