Education Technology

# Activities

9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Software

Cabri Geometry™
TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 10 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

• ##### Report an Issue

Special Parallelograms

#### Activity Overview

In this activity, students will study special types of parallelograms like rhombus and rectangle, and investigate properties related to their diagonals.

#### Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

• TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
• TI-Navigator™  "send to class" feature
• See the attached PDF file for detailed instructions for this activity
• Print pages 41 - 43 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

Rhombus:

• Draw a segment AC, construct its perpendicular bisector, and label the point of intersection as X
• With X as center and XC as radius, draw a circle
• Label the points of intersection of the circle and the perpendicular bisector as B and D
• Hide the circle and connect the points A, B, C, and D to form rhombus ABCD
• Measure the angles of the rhombus
• Observe that the diagonals bisect the opposite angles
• Alter the rhombus and verify this observation
• If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles

• Rectangle:
• Draw a segment AB and construct a perpendicular line through A
• Place a point C on the perpendicular line through A
• Construct a line perpendicular to AC through C
• Construct a line parallel to line AC through point B, and label the point of intersection as D
• Hide lines AC, CD, and BD
• Draw the diagonals of the rectangle
• Measure the diagonals and note that they are congruent
• Alter the rectangle and verify this observation
• If a parallelogram is a rectangle, then the diagonals are congruent
• #### After the Activity

Review student results:

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