Big Idea:

Big Idea 2

Angle relationships determine properties about triangles.

1 week

Evidence of Understanding

  • explore and prove qualities about the interior and exterior angles of any triangle
    • use examples and nonexamples to determine when an angle within a triangle can be classified as interior or exterior
    • analyze examples to justify that interior angles always add up to 180°  and the exterior angles add up to 360°  and attempt to create counterexamples
      • use tools to draw triangles and measure angles, and explain the impact of human error in this process
      • describe and classify triangles based on their angle measures (right, acute, obtuse)
    • describe how the relationships between interior angles of a triangle impact its corresponding side lengths and classification (equilateral, isosceles, scalene)
    • use deductive reasoning to prove that, for any triangle, the three interior angles add up to 180°  and the three exterior angles add up to 360°
      • draw or construct auxiliary lines and apply the properties of parallel lines
    • find the values of missing interior angles of a triangle
       
  • identify and describe relationships between the interior and exterior angles of a triangle
    • analyze examples to justify thatthe exterior angle is always equal to the sum of the two remote angles  and attempt to create counterexamples
    • use deductive reasoning to prove that the exterior angle is always equal to the sum of the two remote angles
      • describe the reflexive and transitive properties when using triangle sum and linear pair in the proof
    • find the measure of missing interior or exterior angles

Develop conceptual understanding:

Interior, exterior, triangle, isosceles, equilateral, scalene, right, acute, obtuse, example, nonexample, interior angles of a triangle, exterior angles of a triangle, remote interior angles (non-adjacent interior angles), auxiliary line, counterexample

Supporting terms to communicate:

side lengths, angle measure, congruent, construct, supplementary, complementary, congruent, straight angles, reflexive property, transitive property, substitute, adjacent
Core Resource
A core resource supports multiple days of instruction. COMING SOON!