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### Math

## Common Core Math

# High School: Geometry: Expressing Geometric Properties with Equations

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.

- Circle equation review
- Features of a circle from its expanded equation
- Features of a circle from its expanded equation
- Features of a circle from its graph
- Features of a circle from its graph
- Features of a circle from its standard equation
- Features of a circle from its standard equation
- Graph a circle from its expanded equation
- Graph a circle from its features
- Graph a circle from its standard equation
- Graphing a circle from its standard equation
- Graphing circles from features
- Write standard equation of a circle
- Writing standard equation of a circle

Derive the equation of a parabola given a focus and directrix.

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

- Center & radii of ellipses from equation
- Ellipse standard equation & graph
- Equation of a hyperbola from features
- Equation of an ellipse from features
- Foci of a hyperbola from equation
- Foci of an ellipse from equation
- Foci of an ellipse from radii
- Graph & features of ellipses
- Vertices & direction of a hyperbola

Use coordinates to prove simple geometric theorems algebraically.

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

- Parallel & perpendicular lines from equation
- Parallel & perpendicular lines from graph
- Parallel & perpendicular lines from graph
- Parallel lines from equation
- Parallel lines from equation (example 2)
- Parallel lines from equation (example 3)
- Perpendicular lines from equation
- Proof: parallel lines have the same slope
- Proof: perpendicular lines have opposite reciprocal slopes
- Prove slope theorems
- Write equations of parallel & perpendicular lines
- Writing equations of perpendicular lines
- Writing equations of perpendicular lines (example 2)

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.