Big Idea:

Big Idea 3

Two triangles can be proven congruent based on the order of their corresponding, congruent sides and angles.

1 week

Evidence of Understanding

  • describe the criteria for congruence and justify why corresponding parts of congruent triangles must be congruent (CPCTC)
    • identify corresponding parts of congruent triangles
    • write congruence statements based on notations in a diagram
    • re-draw and re-orient diagrams to highlight corresponding parts of congruent triangles
  • prove two triangles are congruent
    • explain the congruence between two triangles using rigid motion transformations or constructions
    • identify corresponding congruent parts and apply the criteria of SSS, SAS, ASA, or AAS
      • prove two right triangles are congruent when corresponding Hypotenuse-Leg (HL) are congruent
    • discern when and how to use definitions and the transitive and reflexive properties to establish necessary criteria to prove two triangles are congruent
  • decompose polygons, parallelograms, and triangles to prove congruence
    • prove that the base angles of an isosceles triangle are congruent
      • apply CPCTC to prove that the opposite angles (base angles) of the given sides are congruent
    • prove a parallelogram is composed of two congruent triangles
      • explore and describe when a parallelogram is composed of four congruent triangles
    • prove that a regular hexagon is composed of 6 congruent, equilateral triangles

Develop conceptual understanding:

corresponding parts of congruent triangles are congruent (CPCTC), SSS, ASA, AAS, SAS, Hypotenuse-Leg, base angles, perpendicular bisector, opposite angle/side, parallelogram


Supporting terms to communicate:

corresponding, construct, rotate, reflect, translate, triangle, isosceles, equilateral, scalene, right, acute, obtuse, congruence, equidistant, reflexive property, transitive property, parallel
Core Resource

A core resource supports multiple days of instruction.

Instructional Routine: Sharing Skepticism

The primary goal of this instructional routine is to support students in constructing and critiquing mathematical arguments.