Big Idea:

Big Idea 5

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

1 week

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.