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 3

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

1 week
See Standards
Common Core: Major Standards:
G-CO.B.7

Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

G-CO.C.10

Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Clarification: Theorems include but are not limited to the listed theorems. Example: an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle

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.

  • Congruent Triangles
    This incomplete Core Resource supports students in being able to develop triangle congruence proofs.
    Resource:
    Congruent Triangles

    Geometry & Algebra II Archive

    Geo U2: Proofs about Congruence

    Big Idea: Big Idea 3

    This incomplete Core Resource supports students in being able to develop triangle congruence proofs.

    Preview ResourceAdd a Copy of Resource to my Google Drive
    Type
    Geometry: Proofs About Congruence
    File
    Google Doc
    Tags
    congruent triangles
    Standards
    Common Core: Major Standards ( G-CO.B.7, G-CO.C.10 )
    +— Details
    Common Core: Major Standards:
    G-CO.B.7

    Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

    G-CO.C.10

    Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Clarification: Theorems include but are not limited to the listed theorems. Example: an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle

    All Resources From:
Instructional Routine: Sharing Skepticism

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

  • Isosceles Triangles
    Students use triangle congruence proofs to show that two angles are congruent.
    Resource:
    Isosceles Triangles

    Geometry & Algebra II Archive

    Geo U2: Proofs about Congruence

    Big Idea: Big Idea 3

    Students use triangle congruence proofs to show that two angles are congruent.

    Preview ResourceAdd a Copy of Resource to my Google Drive
    Type
    Geometry: Proofs About Congruence
    File
    Google Doc
    Tags
    congruent triangles, isosceles, instructional routine
    Standards
    Common Core: Major Standards ( G-CO.B.7, G-CO.C.10 )
    +— Details
    Common Core: Major Standards:
    G-CO.B.7

    Understand congruence in terms of rigid motions. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

    G-CO.C.10

    Prove geometric theorems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Clarification: Theorems include but are not limited to the listed theorems. Example: an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle

    All Resources From: