# Rectangle - Definitions and Constructions

***************************************************************************** Our minimal definition: Rectangle – a quadrilateral with three right angles ***************************************************************************** Construct a rectangle. Then observe other constructions and answer the questions below.

What is the definition on which your construction is based?

## Other rectangle constructions

If you want to follow the construction steps, use the navigation buttons at the bottom to scroll through the steps. If you want to see the description/definition of an object, right click it (control+click on Mac).

## Construction 1:

C1: What is the definition used in this construction?

## Construction 2:

C2. What is the definition used in this construction?

## Construction 3:

C3. What is the definition used in this construction?

## ++++++++++ Your own definition(s) ++++++++++++++

Before reading on, spend a few minutes playing with GeoGebra and try to come up with your own definition(s) of a rectangle. For example, can you define rectangle as a special case of trapezoid or parallelogram? etc. Is your definition valid? Is it minimal? Is it equivalent to our minimal definition?

## Construction 4:

This is a "reverse" question. Given the definition below, decide if it is a valid definition of a rectangle, equivalent to our minimal definition. You may want to construct it strictly from the definition and then play with your construction to formulate your conclusion. *********************************************************************************************** A trapezoid with two right angles at one of its bases*. *********************************************************************************************** * Bases of a trapezoid are the two sides that are parallel by the definition.

C4. Is this a valid definiton of a rectangle equivalent to our minimal definition?

## Construction 5:

This is a "reverse" question. Given the definition below, decide if it is a valid definition of a rectangle, equivalent to our minimal definition. You may want to construct it strictly from the definition and then play with your construction to formulate your conclusion. *********************************************************************************************** A quadrilateral with mutally bisecting* congruent diagonals. *********************************************************************************************** * This means that diagonals intersect at their midpoints.