Big Idea:

Big Idea 1

Congruent segments have equal measure.

1 week

Evidence of Understanding

  • describe the qualities that make two line segments congruent or incongruent
    • given any two objects (non-geometric), describe what is the same and different about them
      • Example: a pen and a pencil
    • identify and justify why two objects are the same or different
      • distinguish “exactly the same” from “alike”
    • discuss the difference between points, lines, rays, and line segments in terms of congruence
      • demonstrate how a straight line segment can be drawn joining any two points (Euclid’s first postulate)
      • demonstrate how any straight line segment can be extended indefinitely in a straight line (Euclid’s second postulate)
    • justify which qualities are significant or insignificant for determining if two segments in geometry are congruent
      • Example: length measure vs.color of the segment, thickness, etc.
  • define radius as a relationship between a circle’s center and points on the circle
    • use the compass points to justify that all radii are equidistant and congruent
      • explain how given any straight lines segment, a circle can be drawn having the segment as radius and one endpoint as center (Euclid’s third postulate).
         
  • construct congruent segments and justify their congruence
    • given a line segment, create a congruent segment, and explain why they are congruent
      • use notation to signify congruence
    • describe how a compass can be used to construct congruent segments
      • justify that two segments take up the same distance in space
      • consider and describe implications of human error
    • bisect a line segment and justify congruence of both parts
      • explain that the midpoint bisects a line segment
      • use segment addition to explain that each part is half the measure of the whole
    • compare methods for determining congruence and describe advantages of each type
      • Examples: paper folding, placing the segment (vertical and horizontal only) on the coordinate grid, using patty paper or online software to translate, rotate, or reflect image, etc.

Develop conceptual understanding:

congruent, incongruent, point, line, ray, line segment, postulate, length measure, circle, radius, equidistant, distance, bisect, midpoint, segment addition

Supporting terms to communicate:

compass, straightedge, construction, collinear, coplanar, plane, space, partition, centerpoint, arc, coordinate grid
Core Resource
A core resource supports multiple days of instruction.
  • Introduction to Constructions
    This multiple-day resource introduces students to constructions with a compass and straightedge.
    Resource:
    Introduction to Constructions

    The objective of this activity is to support students with becoming comfortable making precise circles and line segments using a compass and a straight-edge or a ruler.

    All Resources From: