1. PROVING A TRIANGLE IS AN ISOSCELES TRIANGLE
In order to prove a triangle is an isosceles triangle, you must use the distance formula to show 2 sides are congruent in length.
CONCLUSION: This is an isosceles triangle because 2 sides are equal

2. Proving a triangle is a right triangle
You must find the slope of 2 sides, showing they have negative reciprocal slopes, thus proving the 2 sides are ⫠.
CONCLUSION: This is a right triangle because the slopes of 2 sides are ⫠.

3. Proving a triangle is an isosceles right triangle
You must find the lengths of 2 sides, then,
using the coordinates for the same 2 sides, plug them into the slope formula to show their slopes are negative reciprocals, proving the 2 sides are ⫠.
CONCLUSION: This is an isosceles right triangle because the lengths of 2 sides are equal and they have negative reciprocal slopes.