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 5

A quadrilateral can be classified based on the relationship between its diagonals.

1 week
See Standards
Common Core: Major Standards:
G-CO.C.9

Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

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

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.

Common Core: Supporting Standards:
G-CO.D.13

Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Evidence of Understanding

  • investigate the relationship between the diagonals of a quadrilateral and its other characteristics
    • analyze examples and nonexamples to make conjectures about diagonals belonging to parallelograms, rectangles, squares, trapezoids, kites, and rhombuses
      • use constructions, paper folding, and other tools to justify diagonals: of a parallelogram bisect each other, of a rectangle are congruent, and kites are perpendicular
      • construct a square inscribed in a circle using perpendicular bisectors
    • prove diagonals of parallelograms bisect each other
      • prove the converse statement (if diagonals bisect each other then it is a parallelogram)
      • use CPCTC to deductively prove the diagonals intersect at their midpoint
    • prove diagonals of rectangles are congruent
      • investigate diagonals of an isosceles trapezoid and use them show the converse statement is false
    • prove diagonals of a rhombus perpendicularly bisect one another
      • demonstrate perpendicular diagonals do not necessarily bisect one another (ex: kites)
    • find the measure of the missing length of a diagonal

Develop conceptual understanding:

parallelogram, rectangle, square, trapezoid, kite, rhombus, inscribed

Supporting terms to communicate:

trapezoid, diagonal, congruent, bisect, perpendicular, midpoint, segment, sides, lengths, measure, CPCTC, converse, polygon, pentagon, hexagon, octagon, interior angle, exterior angle
Core Resource

No Core Resource for this Big Idea.

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

    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.
    • Partitions of Polygons
      Use the structure of the equations to match a partitioned polygon to the equation that represents the partition.
      Resource:
      Partitions of Polygons

      Geometry & Algebra II Archive

      Geo U2: Proofs about Congruence

      Big Idea: Big Idea 5

      Use the structure of the equations to match a partitioned polygon to the equation that represents the partition.

      Preview ResourceAdd a Copy of Resource to my Google Drive
      Type
      Geometry: Proofs About Congruence
      File
      Google Doc
      Tags
      instructional routine, connecting representations
      Standards
      Common Core: Major Standards ( G-CO.C.9, G-CO.C.10, G-CO.C.11 ) Common Core: Su…
      +— Details
      Common Core: Major Standards:
      G-CO.C.9

      Prove geometric theorems. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

      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

      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.

      Common Core: Supporting Standards:
      G-CO.D.13

      Make geometric constructions. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

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