Big Idea:

Big Idea 1

Relationships between angles determine whether lines are parallel.

1 week

Evidence of Understanding

  • describe the relationship between angles formed by two intersecting lines
    • use tools to explore and describe linear pairs and vertical angles
      • Discuss the impacts of human error
    • justify, using transformations and constructions, that vertical angles are congruent
    • use the angle addition postulate to show why supplementary angles sum to 180
    • deductively prove vertical angles must be congruent using the reflexive and transitive properties
      • explain and apply the subtraction property of equality (Euclid’s third common notion)
    • find the measure of an angle using complementary, supplementary, or vertical pairs
  • explore angle relationships formed by a transversal and a pair of parallel lines
    • use tools to make conjectures about parallel lines with a transversal
      • use constructions and transformations (and other tools) to map angles to each other
      • construct two congruent angles using a rigid motion transformation and parallel lines
      • measuring many pairs of angles and generalizing findings to justify when two angles are congruent or supplementary
    • prove that two lines are parallel using congruent angle relationships (the converse statement)
    • apply properties of vertical angles and linear pairs to prove that two angles are congruent or supplementary
    • create shared definitions for corresponding, alternate interior, alternate exterior, same-side interior or same-side exterior angles (also referred to as consecutive interior or consecutive exterior angles)
    • find the measure of a missing angle

Develop conceptual understanding:

linear pair, supplementary, vertical angles, reflexive property, transitive property, complementary, parallel, transversal, corresponding, alternate interior, alternate exterior, same-side (or consecutive) interior angles, same-side (or consecutive) exterior angles

Supporting terms to communicate:

adjacent, opposite, perpendicular, bisect, degree measure, human error, sum, equal measure, congruent, construct, rotate, translate, reflect, map, carry onto
Core Resource
A core resource supports multiple days of instruction.
  • Relationships Between Angles
    This multiple-day resource supports students in seeing relationships between lines and angles.
    Relationships Between Angles

    The goal of these activities are to help students see that the ways lines and line segments are arranged with respect to each other lead to relationships between the angles formed by those lines and line segments.

    All Resources From:
Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.