Tools of Geometry

12 Components
Initial Task
Transformer
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Representing & Combining Transformations
Re-engagement
Re-engagement for Unit 1
End of Unit Assessments
End of Unit Assessment for Unit 1 Performance Task for Unit 1 End of Unit Assessment Teacher Resources for GEO Unit 1 Find aligned Regents questions with Quiz Banker
Geo U1: Tools of Geometry
Browse Components
Initial Task
Transformer
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Representing & Combining Transformations
Re-engagement
Re-engagement for Unit 1
End of Unit Assessments
End of Unit Assessment for Unit 1 Performance Task for Unit 1 End of Unit Assessment Teacher Resources for GEO Unit 1 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 3

Congruent parts of a polygon map to its congruent parts under a rotation or reflection.

1 week
See Standards
Common Core: Supporting Standards:
G-CO.A.3

Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Clarification: Trapezoid is defined as “A quadrilateral with at least one pair of parallel sides.”

G-CO.D.12

Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Clarification: Constructions include but are not limited to the listed constructions. Example: constructing the median of a triangle or constructing an isosceles triangle with given lengths.

G-CO.D.13

Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Evidence of Understanding

  • describe qualities of polygons
    • use examples and non-examples to justify a figure is a polygon
    • distinguish irregular and regular polygons using congruent sides and congruent angles
    • create and justify all of the lines of symmetry for a regular polygon (use paper folding, drawing, reflective devices, etc.)
    • use isosceles triangles to understand qualities about regular polygons
      • decompose regular polygons into congruent triangles
      • use properties of circles to construct an equilateral triangle
      • use properties of circles to construct a regular hexagon inscribed in a circle
  • explore congruent parts of regular polygons using lines of reflection and center of rotation
    • demonstrate how rotational symmetry and line symmetry carry a polygon onto itself
      • describe rotations as preserving congruence (isometry) and orientation
    • use tools to justify that the line of symmetry, or line of reflection, is the perpendicular bisector
      • construct the perpendicular bisector
      • explain that the distance of each point of the figure from the line of reflection (line of symmetry) is the same
    • generalize qualities about regular polygons using rotational and line symmetry
      • Example: connect lines of symmetry with congruent parts within a polygon and the degree of rotation that carries a polygon onto itself
    • specify the reflection or rotation that carries a polygon onto itself
      • calculate the degree measures that can carry a polygon onto itself
      • use the coordinate plane to write the equation of a horizontal or vertical line that carries a polygon onto itself

Develop conceptual understanding:

polygon, regular polygon, irregular polygon, equilateral, inscribed, rotate, reflect, rotational symmetry, line symmetry, isometry, orientation, line of symmetry, line of reflection, perpendicular bisector

Supporting terms to communicate:

examples, non-examples, congruent, side, angle, triangle, square, pentagon, octagon, preserve, perpendicular, bisect, degree measure, clockwise, counterclockwise

Core Resource

A core resource supports multiple days of instruction.

  • Matching Polygons
    This incomplete Core Resource is designed to support students in making connections between transformations and polygons.
    Resource:
    Matching Polygons

    Geometry & Algebra II Archive

    Geo U1: Tools of Geometry

    Big Idea: Big Idea 3

    This incomplete Core Resource is designed to support students in making connections between transformations and polygons.

    Preview ResourceAdd a Copy of Resource to my Google Drive
    Type
    Geometry: Tools of Geometry
    File
    Google Doc
    Tags
    constructions, polygons, transformations
    Standards
    Common Core: Supporting Standards ( G-CO.A.3, G-CO.D.12, G-CO.D.13 )
    +— Details
    Common Core: Supporting Standards:
    G-CO.A.3

    Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
    Clarification: Trapezoid is defined as “A quadrilateral with at least one pair of parallel sides.”

    G-CO.D.12

    Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Clarification: Constructions include but are not limited to the listed constructions. Example: constructing the median of a triangle or constructing an isosceles triangle with given lengths.

    G-CO.D.13

    Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

    All Resources From:
Instructional Routine: Sharing Skepticism

The primary goal of this instructional routine is to support students in constructing and critiquing mathematical arguments.

  • Counting Triangles
    Students will use transformations implicitly to count the number of shaded triangles in a diagram. During sharing of strategies and through annotation, the transformations used will be made explicit.
    Resource:
    Counting Triangles

    Geometry & Algebra II Archive

    Geo U1: Tools of Geometry

    Big Idea: Big Idea 3

    Students will use transformations implicitly to count the number of shaded triangles in a diagram. During sharing of strategies and through annotation, the transformations used will be made explicit.

    Preview ResourceAdd a Copy of Resource to my Google Drive
    Type
    Geometry: Tools of Geometry
    File
    Google Doc
    Tags
    construct viable argument, transformations, congruence, counting, instructional routine
    Standards
    Common Core: Supporting Standards ( G-CO.A.3, G-CO.D.12, G-CO.D.13 )
    +— Details
    Common Core: Supporting Standards:
    G-CO.A.3

    Experiment with transformations in the plane. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
    Clarification: Trapezoid is defined as “A quadrilateral with at least one pair of parallel sides.”

    G-CO.D.12

    Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Clarification: Constructions include but are not limited to the listed constructions. Example: constructing the median of a triangle or constructing an isosceles triangle with given lengths.

    G-CO.D.13

    Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

    All Resources From: