Outline
Expressing Geometric Properties with Equations (GPE) Cluster
MAFS.912.G-GPE.1.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
MAFS.912.G-GPE.2.4 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, 3) lies on the circle centered at the origin and containing the point (0, 2).
MAFS.912.G-GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
MAFS.912.G-GPE.2.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
MAFS.912.G-GPE.2.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Table of Contents
MAFS.912.G-GPE.1.1
MAFS.912.G-GPE.2.4
- Parallelogram Creation Exercises (I)
- Parallelogram Creation Exercise (II)
- Parallelogram Creation Exercise (III)
- Parallelogram: Coordinate Geometry Setup
- Parallelogram Diagonals
- Isosceles Triangle Medians
- Rectangle Diagonals
- Isosceles Trapezoid Diagonals
- Isosceles Trapezoid Midpoints
- Rhombus Diagonals
- Inscribed Angle Intercepts Semicircle
- 3 Special Points!
- Finsler-Hadwiger Exercise (VA)
- Finsler-Hadwiger Exercise (VB)
- Slope to Angle Measure Calculator (I)
- Slope to Angle Measure Calculator (II)
MAFS.912.G-GPE.2.5
- Rise & Run (Revamped)
- Rise & Run
- Slope: Intuitive Introduction
- Slope: Intuitive Introduction (II)
- Slope: Intuitive Intro and Exploration
- Parallel Consequence? (VA)
- Parallel Consequence? (VB)
- Parallel Lines in the Coordinate Plane (VA)
- Parallel Lines in the Coordinate Plane (VB)
- Coordinate Geometry: Quick Investigation
- Parallel and Perpendicular Lines in the Coordinate Plane
- Perpendicular Lines Investigation (VA)
- Perpendicular Lines Investigation (VB)
- Slope Triangle Rotation (VA)
- Animation 103
- Parallel & Perpendicular Consequence
- Parallel Lines Definition
- Perpendicular Lines Definition (& Consequence)
- Writing Equations of Parallel and Perpendicular Lines
MAFS.912.G-GPE.2.6
MAFS.912.G-GPE.2.7