Big Idea:

Big Idea 4

Corresponding parts of congruent polygons are congruent.

1 week

Evidence of Understanding

  • describe qualities that make two polygons congruent or incongruent
    • identify corresponding parts (angles and sides) of polygons by annotating or redrawing
      • use tools (patty paper, paper folding, etc. to informally translate, reflect and/ or rotate) to map congruent polygons and place them “on top of” each other
      • use notation to signify congruence
    • use examples and non-examples to justifythat corresponding parts of congruent polygons and triangles are congruent (abbreviated as CPCTC for triangles)
    • explore whether equal perimeters or areas mean figures are congruent (or vice versa: if figures are congruent then decide if their perimeters or areas are equal)
       
  • justify two polygons are congruent using rigid motion transformations
    • justify, using tools, how congruent parts match after a rigid motion transformation
      • use notations to show corresponding parts between the pre-image to the image
      • use coordinate notation with the plane to describe rigid motion transformations
    • identify and use thecenter, degree, and direction of rotation to map a pre-image with its corresponding image
    • identify and use the line of reflection to map a pre-image with its corresponding image
      • generate or apply the equation of the line of reflection in the coordinate plane
      • use perpendicular bisectors to draw the line of reflection between a pre-image and its image, or draw the reflected image from a given pre-image and the line of reflection
    • translate an image and justify the preservation of distance and orientation
      • translate an angle by constructing parallel lines
      • determine the translation vector between an image and pre-image (in space or the coordinate plane)
         
  • prove two figures are congruent using a sequence of transformations
    • describe the transformations that carry one figure onto another figure
    • draw transformed images given a sequence of transformations performed on a pre-image

Develop conceptual understanding:

corresponding parts, rigid motion transformations, center of rotation, perpendicular bisectors, pre-image, image, line of reflection, translation vector, parallel lines, sequence of transformations

Supporting terms to communicate:

polygon, translate, reflect, rotate, clockwise, counter-clockwise, congruent, map, carry, construct, function notation, input, output, preserve, orientation
Core Resource

A core resource supports multiple days of instruction.

  • Transforming Polygons
    This incomplete Core Resource supports students in extending what they know about transformations to transform general polygons.
    Resource:
    Transforming Polygons

    This incomplete Core Resource supports students in extending what they know about transformations to transform general polygons.

    All Resources From:
Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.
  • Reflections, Translations, Graphs, and Sentences
    Use visual structure of transformations for triangles to connect with sentence descriptions of transformations.
    Resource:
    Reflections, Translations, Graphs, and Sentences

    Use visual structure of transformations for triangles to connect with sentence descriptions of transformations.

    All Resources From: