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Common Core (Geometry)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to 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).

**Rectangle Proof on Coordinate Plane**

Common Core State Standard G-GPE.4.

Proof that given coordinates on a coordinate plane form a rectangle.
**Circle Proof on Coordinate Plane**

Common Core State Standard G-GPE.4.

Proof that a coordinate lies on a circle with a given center and radius.

**Introduction to Coordinate Proof**

Strategies for placing figures in the coordinate plane

Use the origin as a vertex, keeping the figure in quadrant 1

Center the figure at the origin

Center a side of the figure at the origin

Use one or both axes as sides of the figure

Example 1: Positioning a Figure in the Coordinate Plane

Example 2: Writing a proof in Coordinate Geometry

Example 3: Assigning Coordinates to vertices

Example 4: Writing a Coordinate Proof.**How to Write Coordinate Proofs | Geometry How to Proof Help**

This video models how to place a figure in the coordinate plane and how to write coordinate proofs.

Writing coordinate proofs requires a knowledge of the slope formula, the distance formula and the mid point formula.

Rectangle, Parallelogram, Trapezoid.**Triangles and Coordinate Proof**

Placing triangles on the coordinate plane

1. Use the origin as a vertex or the center of a triangle.

2. Place at least one side of the triangle on an axis.

3. Keep the triangle within the first quadrant if possible.

4. Use coordinates that make computations as simple as possible.

Write a coordinate proof to show that a line segment joining the midpoints of the two sides of a triangle is parallel to the third side. (Midsegment Theorem)**Coordinate Proofs**

Write a coordinate proof to show that the medians to the legs of an isosceles triangle are congruent.**Coordinate Proof for Quadrilaterals:**

Parallelogram, Square, Rectangle, Trapezoid.

Common Core (Geometry)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to 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).

Common Core: HSG-GPE.B.4

Common Core State Standard G-GPE.4.

Proof that given coordinates on a coordinate plane form a rectangle.

Common Core State Standard G-GPE.4.

Proof that a coordinate lies on a circle with a given center and radius.

Strategies for placing figures in the coordinate plane

Use the origin as a vertex, keeping the figure in quadrant 1

Center the figure at the origin

Center a side of the figure at the origin

Use one or both axes as sides of the figure

Example 1: Positioning a Figure in the Coordinate Plane

Example 2: Writing a proof in Coordinate Geometry

Example 3: Assigning Coordinates to vertices

Example 4: Writing a Coordinate Proof.

This video models how to place a figure in the coordinate plane and how to write coordinate proofs.

Writing coordinate proofs requires a knowledge of the slope formula, the distance formula and the mid point formula.

Rectangle, Parallelogram, Trapezoid.

Placing triangles on the coordinate plane

1. Use the origin as a vertex or the center of a triangle.

2. Place at least one side of the triangle on an axis.

3. Keep the triangle within the first quadrant if possible.

4. Use coordinates that make computations as simple as possible.

Write a coordinate proof to show that a line segment joining the midpoints of the two sides of a triangle is parallel to the third side. (Midsegment Theorem)

Write a coordinate proof to show that the medians to the legs of an isosceles triangle are congruent.

Parallelogram, Square, Rectangle, Trapezoid.

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