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Common Core: Math
CCLS - Math: G.GPE.4
- Expressing Geometric Properties With Equations
- Use Coordinates To Prove Simple Geometric Theorems Algebraically
- State Standard:
- 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, √3) lies on the circle centered at the origin and containing the point (0, 2).
- Student Outcomes Given a circle, students find the equations of two lines tangent to the circle with specified slopes. Given a circle and a point outside the circle, students find the equation of the...
- Topic D brings in coordinate geometry to establish the equation of a circle. Students solve problems to find the equations of specific tangent lines or the coordinates of specific points of contact...
- Geometry Module 5: Circles With and Without Coordinates This module brings together the ideas of similarity and congruence and the properties of length, area, and geometric constructions studied...
- Student Outcomes: Students name several points on a line given by a parametric equation and provide the point-slope equation for a line given by a parametric equation. Students determine whether...
- Student Outcomes: Using coordinates, students prove that the intersection of the medians of a triangle meet at a point that is two-thirds of the way along each median from the intersected vertex....
- Student Outcomes: Students find midpoints of segments and points that divide segments into 3, 4, or more proportional, equal parts.
- Students find midpoints of segments and points that divide segments into 3 or more equal and proportional parts and extend this concept prove classical results in geometry. Students are introduced...
- Student Outcomes: Students recognize parallel and perpendicular lines from slope. Students create equations for lines satisfying criteria of the kind: “Contains a given point and is parallel/...
- Student Outcomes: Students explain the connection between the Pythagorean Theorem and the criterion for perpendicularity.
- The challenge of programming robot motion along segments parallel or perpendicular to a given segment leads to an analysis of slopes of parallel and perpendicular lines. Students write equations for...
- Geometry Module 4: Connecting Algebra and Geometry Through Coordinates In this module, students explore and experience the utility of analyzing algebra and geometry challenges through the framework...