1. 2.4 Classifying Figures on a Coordinate Grid
Part I: Classifying Triangles
Scalene (no sides equal)
Isosceles (two sides equal)
Equilateral (all sides equal)
Right (two sides are perpendicular)

2. Triangle Classification
Required Calculation
Required Result
Scalene Triangle
lengths of all sides
All sides have different lengths
Isosceles Triangle
Exactly two sides have the same length
Equilateral Triangle
All sides have the same length
Right Triangle
lengths of all sides or
slopes of all sides
Side lengths satisfy the Pythagorean Theorem or two sides are perpendicular

3. Example 1: A triangle has vertices P(2, 1), Q(-1, -3) and R(6, -2)
Example 1: A triangle has vertices P(2, 1), Q(-1, -3) and R(6, -2). Is the triangle scalene, isosceles, or equilateral? Is ∆PQR a right triangle? P Q R

4. Example 1: A triangle has vertices P(2, 1), Q(-1, -3) and R(6, -2)
Example 1: A triangle has vertices P(2, 1), Q(-1, -3) and R(6, -2). Is the triangle scalene, isosceles, or equilateral? Is ∆PQR a right triangle? P Q R

5. Quadrilateral Classification
Part 2: Classifying Quadrilaterals
If you were given the co-ordinates of the four vertices of a quadrilateral, what calculations would you perform to determine what kind of quadrilateral it is?
Quadrilateral Classification
Required Calculation
Required Result
Parallelogram
Find the lengths of all four sides
Find the slope of two adjacent sides
Opposite sides equal in length
Adjacent slopes are not negative reciprocals
Rhombus
All sides the same length x x

6. Quadrilateral Classification
Required Calculation
Required Result
Square
Find the lengths of all four sides
Find the slope of two adjacent sides
All sides the same length
Adjacent slopes are negative reciprocals
Rectangle
Opposite sides equal in length

7. Example 2: Determine the type of quadrilateral described by the vertices A(3,-4), B(9,2), C(14,-3) and D(8,-9). A B C D

8. Example 2: Determine the type of quadrilateral described by the vertices A(3,-4), B(9,2), C(14,-3) and D(8,-9). A B C D