Secondary Mathematics II
Educational Links

Strand: GEOMETRY - Expressing Geometric Properties With Equations (G.GPE)

Translate between the geometric description and the equation for a conic section (Standard G.GPE.1). Use coordinates to prove simple geometric theorems algebraically. Include simple proofs involving circles (Standard G.GPE.4). Use coordinates to prove simple geometric theorems algebraically (Standard G.GPE.6).

Standard G.GPE.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).

• Coordinates of equilateral triangles
  The purpose of this Illustrative Mathematics task is to examine angles of triangles whose vertices have specific integer coordinates.
• Finding Equations of Parallel and Perpendicular Lines
  This lesson unit is intended to help educators assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines.
• GEOMETRY - Expressing Geometric Properties With Equations (G.GPE) - Sec Math II Core Guide
  The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics II - Expressing Geometric Properties with Equations (G.GPE).
• Sorting Equations of Circles 2
  This lesson unit is intended to help educators assess how well students are able to translate between the equations of circles and their geometric features, and sketch a circle from its equation.

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http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.