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

Use coordinates to prove simple geometric theorems algebraically (Standards G.GPE.4-5, 7).

Standard G.GPE.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles; connect with The Pythagorean Theorem and the distance formula.

• GeoGebra
GeoGebra is dynamic online geometry software. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards.
• GEOMETRY - Expressing Geometric Properties With Equations (G.GPE) - Sec Math I Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics I - Expressing Geometric Properties with Equations (G.GPE).
• Introduction to the Materials (Math 1)
Introduction to the Materials in the Mathematics One of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
• Module 8: Connecting Algebra & Geometry - Student Edition (Math 1)
The Mathematics Vision Project, Secondary Math One Module 8, Connecting Algebra and Geometry, students use the Pythagorean Theorem to find the distance between two points and to derive the distance formula.
• Module 8: Connecting Algebra & Geometry - Teacher Notes (Math 1)
The Mathematics Vision Project, Secondary Math One Module 8 Teacher Notes, Connecting Algebra and Geometry, students use the Pythagorean Theorem to find the distance between two points and to derive the distance formula.
• Perpendicular Lines video
This video introduces and explains perpendicular lines.
• Squares on a coordinate grid
The purpose of this task is to use the Pythagorean Theorem and knowledge about quadrilaterals in order to construct squares of different sizes on a coordinate grid.
• Triangle Perimeters
The purpose of this task is to apply the Pythagorean theorem to calculate distances and areas.

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.