Exploring Geometry

Properties of Rectangles  

How do I do it?

Here's a way to get two perpendicular lines at once. Select segment AB and points A & B; then in the Construct Menu, choose perpendicular l line.

Select a segment; then in the Measure menu, choose Length, OR select two endpoints and choose Distance.

A rectangle is a quadrilateral with four right angles. In this investigation, you'll discover that a rectangle has many special properties besides it equal angles.

 Sketch and Investigate 

First you'll construct a rectangle using its definition.

1. Construct AB

2. Construct lines perpendicular to AB through points A and B.

3. Construct point C on the line through point A.

4. Construct a line through point C perpendicular to AC.

5. Construct the fourth vertex, point D, at the intersection of this line and the line through point B.

6. Hide the lines, then construct segments to complete the rectangle.

7.Measure the sides of a rectangle.

8. Drag different vertices of your rectangle to make sure it's constructed properly. Observe the side lengths as you drag.

9. Construct the diagonals and their point of intersection.

10 Drag parts of the rectangle and observe the diagonals. Measure lengths that look as if they might be related.

Points to Ponder

On a separate sheet of paper, write a conjecture about ...

• the sides of a rectangle.

• the diagonals of a rectangle. 

Going Further & Deeper . . . 
Constructing a Parallelogram

How many ways can you construct a rectangle? Try methods that use the construct menu, the transform menu or combinations of both. Consider how you might use diagonals. Write a brief description of each construction method along with the properties of rectangles that make it work.