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Mathematics - Secondary Curriculum 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.45, 7).
  • 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.
  • Equal Area Triangles on the Same Base I
    This task is an relatively easy application of the formula for the area of a triangle and use of parallel lines.
  • Equal Area Triangles on the Same Base II
    This task has students apply their knowledge of parallel lines to solve a geometric problem on areas of triangles.
  • 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 6: Transformations & Symmetry - Student Edition (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 6, Transformations and Symmetry, builds on students experiences with rigid motion in earlier grades to formalize the definitions of translation, rotation, and reflection.
  • Module 6: Transformations & Symmetry - Teacher Notes (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 6 Teacher Notes, Transformations and Symmetry, builds on students experiences with rigid motion in earlier grades to formalize the definitions of translation, rotation, and reflection.
  • 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.
  • Parallel Lines
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Parallel Lines video
    This video explains the concept.
  • Perpendicular Lines
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Perpendicular Lines video
    This video introduces and explains perpendicular lines.
  • Slope Criterion for Perpendicular Lines
    The goal of this task is to use similar triangles to establish the slope criterion for 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.
  • Triangles inscribed in a circle
    The goal of this task is to use ideas about linear functions in order to determine when certain angles are right angles.
  • Unit Squares and Triangles
    This problem provides an opportunity for a rich application of coordinate geometry.
  • When are two lines perpendicular?
    The goal of this task is to examine when two lines in the plane are perpendicular in terms of their slopes.


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.