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Mathematics - Secondary Curriculum Secondary Mathematics I
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Strand: GEOMETRY - Congruence (G.CO)

Experiment with transformations in the plane. Build on student experience with rigid motions from earlier grades (Standards G.CO.1-5). Understand congruence in terms of rigid motions. Rigid motions are at the foundation of the definition of congruence. Reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems (Standards G.CO.6-8). Make geometric constructions (Standards G.CO.12-13).

Standard G.CO.2

Represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

  • 3D Transmographer
    This lesson contains an applet that allows students to explore translations, reflections, and rotations.
  • Constructions
    This site provides both a video and step-by-step directions on how to complete a variety of constructions.
  • Dilations and Distances
    The goal of this task is to study the impact of dilations on distances between points.
  • Fixed points of rigid motions
    The purpose of this task is to use fixed points at a tool for studying and classifying rigid motions of the plane.
  • GEOMETRY - Congruence (G.CO) - 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 - Congruence (G.CO).
  • Geometry in Tessellations
    In this lesson students will learn about lines, angles, planes, and experiment with the area and perimeter of polygons.
  • Horizontal Stretch of the Plane
    The goal of this task is to compare a transformation of the plane (translation) which preserves distances and angles to a transformation of the plane (horizontal stretch) which does not preserve either distances or angles.
  • Identifying Unknown Transformations
    This applet allows the student to drag a shape and then observe the changes to its behavior. They then determine whether the alteration is due to reflection, a rotation, or a translation/slide transformation.
  • 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.
  • Symmetries of a circle
    This task asks students to examine lines of symmetry using the high school definition of reflections.
  • Tangent Lines and the Radius of a Circle
    This task presents a foundational result in geometry, presented with deliberately sparse guidance in order to allow a wide variety of approaches.
  • Translations, Reflections, and Rotations
    Students are introduced to the concepts of translation, reflection and rotation in this lesson plan.
  • Unit Squares and Triangles
    This problem provides an opportunity for a rich application of coordinate geometry.

UEN logo - 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.