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)

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

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

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

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

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

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

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