Big Idea:

Big Idea 2

Congruent angles have equal angle measure.

1 week

Evidence of Understanding

  • describe qualities that make two angles congruent or incongruent
    • define an angle using its vertex and rays
      • recognize that as an angle measure increases, its arc measure increases
    • define all straight angles as having 180° and are therefore all congruent angle measures
      • show and describe why an angle whose arc measure is 180° is also a semi-circle
      • show and describe why an angle whose arc measure is 360° is also a complete circle
    • justify which qualities are mathematically significant or insignificant for determining if two angles are the same
      • Example: degree measure vs. color of the angle, length of the rays, thickness, etc.
         
  • construct congruent angles and justify their congruence
    • compare methods for determining congruence and describe advantages of each type
      • Examples: paper folding, placing angles on the coordinate grid, using patty paper or online software to translate, rotate, or reflect image, etc.
    • given an angle, create a congruent angle, and explain why they are congruent
      • use notation to signify congruence
      • consider and describe implications of human error
    • bisect an angle and justify congruence of both parts
      • use angle addition to explain that each part is half the degree measure of the whole
      • construct congruent right angles using a perpendicular bisector
         
  • perform constructions and analyze the relationships among the segments or angles created
    • explore congruent relationships between segments and angles formed by constructing a perpendicular bisector
    • describe how two congruent angles are sectors of the same circle, including congruent radii and arc measures

Develop conceptual understanding:

angle, vertex, ray, degree measure, sector of a circle, perpendicular, angle addition, right angle, perpendicular, perpendicular bisector, straight angle

Supporting terms to communicate:

congruent, incongruent, point, line, line segment, length measure, acute, obtuse, circle, arc, radius, equidistant, distance, bisect, midpoint, compass, construction, partition, protractor
Core Resource
A core resource supports multiple days of instruction.
  • Matching Angles
    The goal of this week is for students to revisit what an angle is and explore what makes two angles congruent using a variety of different tools. Students will also complete a series of constructions that relate to angle congruence.
    Resource:
    Matching Angles

    The goal of this week is for students to revisit what an angle is and explore what makes two angles congruent using a variety of different tools. Students will also complete a series of constructions that relate to angle congruence.

    All Resources From: