Properties of Rectangles, Rhombuses and Squares

Author:
Andrea Smith, Alan, Chris Hood
Topic:
Rectangle, Square
In this activity, you will use what you have learned about parallelograms to discover properties about rectangles, rhombuses (rhombi), and squares. As you complete this activity, fill in the blanks on notes on the list of properties for each quadrilateral.
A rectangle is a parallelogram with 4 right angles.
Rectangles also have properties that not all parallelograms possess. Let's discover these additional properties.

Measure the diagonals in the rectangle below by selecting the measurement tool (the button with "cm" and an arrow), then click on each endpoint of the segment you are measuring. The length will appear. What did you discover about diagonals AD and FB? Also, move one of the vertices to change the rectangle (Select the move tool first. The one with the white arrow). Does this change what you discovered? Finish the following sentence on your notes: The diagonals of a rectangle are __________________________.

Applet #1 RECTANGLE

Now, let's explore rhombuses. A rhombus is a parallelgram with 4 congruent sides.
Rhombuses also have properties that not all parallelograms possess. Let's discover these additional properties.

In the rhombus below, measure the angles AHB, BHG, EHG, and AHE (Select the angle tool, then click on the points in order of the name of the angle.) What did you discover? Move one of the vertices to see if your findings remain the same for all rhombuses. Finish the following sentence on your notes: The diagonals of a rhombus are __________________________ to each other.

Applet #3 RHOMBUS

Using the rhombus applet above, measure angles ABH, GBH, GEH, and AEH. What did you discover about these angles? Manipulate the rhombus to see if your findings hold for all rhombuses.

So what does one diagonal do to a pair of opposite angles in a rhombus?

Does the other diagonal do the same thing?

So what do the diagonals of a rhombus do to both pair of opposite angles in a rhombus? Finish the following sentence on your notes: Each diagonal of a rhombus __________________________ opposite angles of the rhombus.

Finally, a square is a parallelogram, rhombus, and a rectangle.

Since a square possesses all the properties of a parallelogram, rectangle, and rhombus, Finish the following sentence on your notes: The diagonals of a square are __________________________. The diagonals of a square are __________________________ to each other. Each diagonal of a square __________________________ opposite angles of the square.

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