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Activity Overview

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

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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
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During the Activity

Distribute the page to the class.

Follow the Activity procedures:

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
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After the Activity

Review student results:

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