given by an equation. G.GPE.4 Use Students can write the equation of the circle being described and then use Ability to connect coordinates to prove substitution to demonstrate the coordinate of the given point satisfy the experience with simple geometric equation of the given circle thus proving that the point lies on the circle. coordinate proofs theorems algebraically.; from Unit 4 to for example prove or circles disprove that the point on the circle (1, √3) lies centered at the origin and containing the point (0, 2). Include simple Note: proofs involving circles. G.MG.1 Use geometric Apply geometric properties of circles to solve modeling problems. Ability to connect shapes, their measures, experiences from and their properties to Unit 2 and Unit 3 describe objects. (e.g., with two- modeling a tree trunk or dimensional and a human torso as a three-dimensional shapes to circles cylinder). ★ Note: Focus on situations in which the analysis of circles is required.
given by an equation. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.; for example prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). Note: Include simple proofs involving circles. Ability to connect experience with coordinate proofs from Unit 4 to circles Students can write the equation of the circle being described and then use substitution to demonstrate the coordinate of the given point satisfy the equation of the given circle thus proving that the point lies on the circle. G.MG.1 Use geometric shapes, their measures, and their properties to describe objects. (e.g., modeling a tree trunk or a human torso as a cylinder). ★ Note: Focus on situations in which the analysis of circles is required. Ability to connect experiences from Unit 2 and Unit 3 with two- dimensional and three-dimensional shapes to circles Apply geometric properties of circles to solve modeling problems.
Geometry_U5_UP_Circles_with_and_Without_Coordinates_jan_11.docx