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

#### Activity Overview

Students construct cyclic quadrilaterals and investigate their properties. They determine which quadrilaterals from the quadrilateral hierarchy are cyclic.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print page 19 from the attached PDF file for your class
• #### During the Activity

Distribute the page to the class.

• Construct a circle and label its center
• Inscribe a quadrilateral within the circle
• Note that the opposite interior angles are supplementary and the perpendicular bisectors of the sides of the quadrilateral are concurrent at a point if, and only if, the quadrilateral is cyclic
• Measure the lengths of the sides and diagonals of the quadrilateral
• Observe that the sum of the products of the two pairs of opposite sides is equal to the product of the diagonals
• Understand that if a parallelogram is cyclic, it has to be a rectangle, and if a rhombus is cyclic, it has to be a square
• Verify the formula for determining the area of a cyclic quadrilateral
• #### After the Activity

Review student results:

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