Discovery of the Properties of Rectangles, Rhombuses and Squares

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, check off your list of properties for each quadrilateral.

A rectangle is a parallelogram with 4 right angles.

Since rectangles are parallelograms, what four properties do rectangles possess?

Rectangles also have properties that not all parallelograms possess. Let's discover these additional properties.

Measure the diagonals in the rectangle below. What did you discover about diagonals AD and FB? Also, move one of the vertices to change the rectangle. Does this change what you discovered?

Are diagonals congruent for all parallelograms or just rectangles? To answer this question, use the parallelogram in the app below. Measure the diagonals AD and CB to see if they are congruent. What did you discover?

In the rectangle below. Measure AH, HD, HF, HB by clicking on their endpoints with the measuring segment tool. What did you discover about the lengths of these segments? Drag one of the vertices to see if if your conclusion holds for all rectangles.

Therefore, not only does a rectangle's diagonals bisect each other, they bisect each other into four congruent segments.

Now, let's explore rhombuses. A rhombus is a parallelgram with 4 congruent sides.

Since a rhombus is a parallelogram, what four properties do rhombuses already possess.

Rhombuses also have more properties.

Using the rhombus below, let's see if the properties we discovered for rectangles are true for rhombuses.

Measure the diagonals in the rhombus below. Do the diagonals bisect each other into 4 congruent segments?

In the rhombus below, measure the angles AHB, BHG, EHG, and AHE. What did you discover? Move one of the vertices to see if your findings remain the same for all rhombuses.

Based on the previous question, what is true about the diagonals of a rhombus?

Using the rectangle below, determine if the diagonals of a rectangle are perpendicular. What did you discover?

Using the rhombus below, 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?

Using the rectangle below, do the diagonals of a rectangle bisect opposite angles? Manipulate the rectangle to see if your findings are true for all rectangles.

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

Since a square possesses all the properties of a parallelogram, rectangle, and rhombus, List all the properties of a square based on what you have discovered in the exercises above.

Discovery of the Properties of Rectangles, Rhombuses and Squares

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