Education Technology

# Activities

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 1 from the EXPLORATIONS Book:
Geometric Investigations on the Voyage 200 with Cabri

## Investigating Properties of Kites

#### Activity Overview

In this activity, students construct kites and investigate their properties. They also relate the properties to squares and rhombi.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print page 1 from the attached PDF file for your class
• #### During the Activity

Distribute the page to the class.

• Determine 3 ways to construct a kite
• Construct a kite using one method
• Determine if non convex kites can be constructed using the method
• Draw the diagonals of a kite
• Observe that the diagonals are perpendicular
• Measure the area of the kite
• Observe that the area is equal to one-half the product of the lengths of its diagonals and is true for convex and non convex kites
• Drag the vertices of the kite and ensure that the relationships are maintained
• Understand that the quadrilateral that connects the consecutive midpoints of a kite will always be a rectangle

• Inscribe the kite in a rectangle such that the end points of the larger diagonal are the mid points of the sides of the rectangle
• Measure the area of the rectangle
• Note that the area of the kite is one-half the area of the rectangle
• Observe that the relationship is true for all location of the vertices of the kite
• Move the position of the vertices on the sides of the rectangle and measure the perimeter of the kite
• Observe that the perimeter is minimum when the vertices lie on the midpoint of the two sides of the rectangle
• Verify algebraically using quadratic function

• Investigate the rhombus and the square; which are specialized kites, and observe that these quadrilaterals display the properties of kites
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary