What Is a Rectangle?
Rectangle definition
For a shape to be a rectangle, it must be a four-sided polygon with two pairs of parallel, congruent sides and four interior angles of 90° each. If you have a shape that matches that description, it also is all this:
A plane figure
A closed shape
A quadrilateral
A parallelogram
The four sides of your polygon, to create two pairs of parallel sides, must also be two congruent pairs. The base and top will be equal in length, and the left and right sides will be equal in length.
Is a rectangle a parallelogram or rhombus?
A parallelogram and rhombus can only be rectangles when their interior angles are each 90°.
Is a square a rectangle?
While a rectangle is a type of quadrilateral, parallelogram, closed shape and plane figure, only a square is always a type of rectangle.
What is a rectangle?
Rectangles are very handy to have around. You see them in bricks, cement blocks, picture frames, posters, sheets of paper, the faces of play bricks that snap together, the sides of shoe boxes and cereal boxes, and a lot of other everyday objects.
Rectangles are great because they stack neatly, since they have two pairs of parallel sides. Their right angles make sure built things (houses, office buildings, schools) stand straight and tall.
You can use four linear (straight) objects to make a rectangle. Make certain two of the objects are the same length, and the other two objects are the same length. Arrange them so the longer pieces are parallel and exactly a distance apart so the other two, shorter pieces can touch their ends.
When all four ends are touching, you may need to adjust to make sure all four inside angles look like right angles, or 90°. Adjacent sides of a rectangle are perpendicular.
Later we will see how to draw a rectangle using a protractor, straightedge (or ruler), and pencil.
Properties of rectangles
The main identifying property of a rectangle is its four interior right angles. You cannot construct a rectangle without those four angles adding to 360° and each measuring 90°. When you do that, the four sides will automatically create the other identifying property.
The other property that identifies rectangles is that opposite sides are congruent and parallel. Congruent means they have the same length; parallel means they are the same distance apart throughout their length.
A rectangle has no restrictions on the lengths of its two pairs of sides; you can have a very long, low rectangle, or a very fat rectangle, or a rectangle with four equal-length sides (that's a square).
How to construct a rectangle
A protractor measures angles. A straightedge (or ruler) makes straight lines. Use the ruler or straightedge to make a straight line segment on a piece of paper, roughly in the lower third of the sheet. That line segment is your base. Align your protractor with that line segment, working at one endpoint at a time.
At each end of the line segment, exactly at the endpoint, mark a 90° angle. Use the straightedge to connect that 90° mark and the endpoint of the line segment. You now have the two sides of the rectangle.
Mark a new endpoint on one of those new sides, at some distance away from your base. Turn the protractor 90° and align it with either side, at the endpoint of that newly drawn side. Mark 90° using the protractor and again use the straightedge to connect the side's endpoint with that new 90° mark.
When that line segment intersects the other side, you have constructed a rectangle.
Of course, if you use a ruler with markings in inches or centimeters, you can measure the length of your base, measure the length of the two sides left and right, and ensure the long, top side is equal to the length of the base.
Either method will accurately and quickly give you a rectangle you constructed by yourself.
Lesson summary
In this lesson, you used the video, drawings and instructions to learn about rectangles. You learned what a rectangle is, how to recognize a rectangle in the world around you, how the rectangle fits into the family of quadrilaterals, and the other shape that is always a rectangle (only the square!).
You also learned two identifying properties of rectangles: all rectangles have two pairs of congruent, parallel sides; and all rectangles have four interior angles of 90° each.
Finally, you learned how to construct your own rectangle using a straightedge, protractor, pencil and paper. You learned a lot!