Lesson Plan

Place geometric figures on a coordinate plane using strategic coordinate assignments to simplify algebraic work

Use the distance formula to verify side lengths and determine whether sides of a figure are congruent

Use slopes to verify whether sides of a figure are parallel or perpendicular

Construct a complete coordinate geometry proof that a given quadrilateral is a rectangle, parallelogram, rhombus, or other specific figure

Prove or disprove that a given point lies on a circle by substituting coordinates into the circle's equation

HSG.GPE.B.4

HSG.GPE.B.4: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, sqrt(3)) lies on the circle centered at the origin and containing the point (0, 2).