Skip Navigation

Utah Core  •  Curriculum Search  •  All Mathematics - Secondary Lesson Plans  •  USBE Mathematics - Secondary website

Mathematics - Secondary Curriculum Secondary Mathematics I
Educational Links

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

Use coordinates to prove simple geometric theorems algebraically (Standards G.GPE.45, 7).

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).

  • A Midpoint Miracle
    This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.
  • 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.
  • Unit Squares and Triangles
    This problem provides an opportunity for a rich application of coordinate geometry.


UEN logo 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.