Education Technology

Special Parallelograms

Published on 06/09/2008

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.

    Follow the Activity procedures:

    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