Tools of Geometry

12 Components
Initial Task
Transformer
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Representing & Combining Transformations
Re-engagement
Re-engagement for Unit 1
End of Unit Assessments
End of Unit Assessment for Unit 1 Performance Task for Unit 1 End of Unit Assessment Teacher Resources for GEO Unit 1 Find aligned Regents questions with Quiz Banker
Geo U1: Tools of Geometry
Browse Components
Initial Task
Transformer
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4 Big Idea 5
Formative Assessment Lesson
Representing & Combining Transformations
Re-engagement
Re-engagement for Unit 1
End of Unit Assessments
End of Unit Assessment for Unit 1 Performance Task for Unit 1 End of Unit Assessment Teacher Resources for GEO Unit 1 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 5

SSS, SAS, and ASA are sufficient criteria to justify triangle congruence.

1 week
See Standards
Common Core: Major Standards:
G-CO.B.6

Understand congruence in terms of rigid motions. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

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.B.8

Understand congruence in terms of rigid motions. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Common Core: Supporting Standards:
G-CO.A.5

Experiment with transformations in the plane. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO.D.12

Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Clarification: Constructions include but are not limited to the listed constructions. Example: constructing the median of a triangle or constructing an isosceles triangle with given lengths.

Evidence of Understanding

  • justify the minimum requirements that show two triangles are congruent
    • describe how a sequence of transformations demonstrates the mapping of corresponding sides for two congruent figures
      • use notations to signify the corresponding parts
    • make conjectures about the minimum corresponding parts of the triangle needed to construct a congruent triangle
      • experiment with constructions to support these claims
      • give examples, non examples, or counterexamples about these claims
      • use transformations of these parts to support their claim that the triangles are congruent
    • justify that when all corresponding sides of two triangles are congruent (SSS) there is sufficient evidence to show that these two triangles are congruent
      • use tools to construct a copy of a given triangle using side measurements
    • justify that when two corresponding sides and the included angle are congruent (SAS) there is sufficient evidence to show that these two triangles are congruent
      • use tools to construct a copy of a given triangle using two side measurements and the included angle
      • establish the the minimum criteria necessary to prove two right triangles are congruent using the hypotenuse and a leg (HL)
    • justify that when two corresponding angles and the included side of two triangles are congruent (ASA) there is sufficient evidence to show that these two triangles are congruent
      • use tools to construct a copy of a given triangle using two angle measurements and the included side
      • justify why the angle has to be the included angle of the corresponding sides using constructions (SSA does not work)

Develop conceptual understanding:

SSS, SAS, HL, ASA

Supporting terms to communicate:

included angle/side, construct, copy, corresponding parts, preserve, congruent, sequence of transformations, rotate, reflect, translate, parallel, perpendicular
Core Resource

No Core Resource for this Big Idea.

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