# Activities

• • • ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 3 from the EXPLORATIONS Book:
Geometric Investigations on the Voyage 200 with Cabri

## Investigating Properties of the Diagonals of Quadrilaterals

#### 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.

• 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