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