12 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
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Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### 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.
• 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

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

All Resources From:
• Unit 2