Proofs about Congruence

12 Components
Initial Task
What's My Angle?
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Analyzing Congruency Proofs
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 Performance Task for Unit 2 End of Unit Assessment Teacher Resources for GEO Unit 2 Find aligned Regents questions with Quiz Banker
Geo U2: Proofs about Congruence
Browse Components
Initial Task
What's My Angle?
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Analyzing Congruency Proofs
Re-engagement
Re-engagement for Unit 2
End of Unit Assessments
End of Unit Assessment for Unit 2 Performance Task for Unit 2 End of Unit Assessment Teacher Resources for GEO Unit 2 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 4

Properties of parallel lines and triangles determine the characteristics of polygons.

1 week
See Standards
Common Core: Major Standards:
G-CO.C.11

Prove geoemtric theorems. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Evidence of Understanding

  • distinguish trapezoids, parallelograms, rectangles, kites, rhombuses, and squares using properties of their sides and angles
    • analyze examples and nonexamples to create and and test conjectures about quadrilaterals
    • identify and use properties that result in quadrilaterals being part of the same “family”
      • Examples: rectangle, square, and rhombus are all parallelograms, and all parallelograms are trapezoids
  • explore and prove relationships about interior and exterior angles of quadrilaterals and regular polygons
    • apply knowledge about triangles to generate and test conjectures about quadrilaterals and other regular polygons
      • use diagonals (auxiliary lines) to partition figures into triangles to determine the the sum of the interior angles of a polygon
    • justify thatinterior angles of a quadrilateral always add up to 360° using examples and non-examples
      • use tools to draw quadrilaterals, measure angles, and explain the impact of human error
    • prove the interior angles for any quadrilateral sum to 360°
    • find the value of missing interior and exterior angles in a polygon
  • explore and prove relationships about angles and sides of a parallelogram
    • identify and justify congruent angles and sides of a parallelogram
      • make conjectures and use dynamic software, index cards, transparencies, paper folding, etc. to study sides and angles
    • prove opposite sides and angles of a parallelogram are congruent
      • apply properties of parallel lines cut by a transversal
    • prove same side/consecutive interior angles of a parallelogram are supplementary
    • prove a given figure is a square, rectangle, or rhombus
      • apply properties of parallelograms, parallel lines, and triangle congruence criteria
    • find the measure of a missing value or measurements

Develop conceptual understanding:

quadrilaterals, rectangle, square, rhombus, parallelogram, trapezoid, kite, diagonal

Supporting terms to communicate:

example, non-example, human error, supplementary, bisect, perpendicular, parallel, transversal, auxiliary line, interior angles, adjacent side/angle, opposite side/angle, SSS, SAS, ASA, AAS, CPCTC
Core Resource

No Core Resource for this Big Idea.

Consider using the Instructional Routines linked below for teaching towards this Big Idea.