Activity Overview
In this activity, students will explore the properties of the diagonals of various quadrilaterals. They will use a quadrilateral hierarchy chart to examine the relationship between the quadrilaterals.
Before the Activity
See the attached PDF file for detailed instructions for this activity
Print page 10 from the attached PDF file for your class
During the Activity
Distribute the page to the class.
Follow the Activity procedures:
Examine a chart displaying quadrilateral hierarchy
Construct different quadrilaterals and investigate their properties
Verify that each quadrilateral in the chart is a special case of the quadrilaterals connected above it
Write down the statements and note that they are true for the figure and all the figures connected below it, but not true for the figures above it in the chart
Understand that the diagonals of an isosceles trapezoid are congruent, but this property does not necessarily hold true for a simple trapezoid
Observe that the diagonals of a kite, rhombus, and a square are perpendicular
Identify that the diagonals of a parallelogram, rhombus, rectangle, and a square bisect each other
Investigate the four triangles formed by the diagonals of the quadrilateral
Note that the product of the areas of opposite triangles formed by the diagonals of a convex quadrilateral are always equal
Adjust the diagonals of a parallelogram until the lengths are congruent to assure that the four corners are square
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary