10.4.1 Everyday Shapes

Notepad iconActivity: Everyday shapes

You are probably already familiar with shapes such as triangles, squares, rectangles, and circles from everyday life. Spend a few moments summarizing what you know about these shapes already, including how you recognize them and where you might find them.

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Triangles have three straight sides and are often used in buildings since they cannot be distorted. For example, they may be used for bracings or supports.

Squares and rectangles both have four straight sides and their angles are all right angles. In addition, the sides of a square are all the same length. These shapes can be seen everywhere—books, tables, tiles, buildings, etc.

Circles can be drawn by specifying a center point and a radius—the distance from the center to the circle’s edge. The radius is always a constant length. The diameter of a circle is the distance from one edge of the circle to the other, passing through the center. The edge of the circle (or the length of this edge) is known as the circumference. Circles are often used where movement is involved (for example, wheels) or where lack of corners is important (for example, cups or bowls). [Why are manhole covers usually rounded? Hint: Think about the possibility of dropping the cover into the hole!]

Don’t worry if you didn't get all these details—you are here to learn! Just take the time to note down any new information to you in your math notebook.

Let's take a more in-depth look triangles and four-sided shapes.

You may have mentioned some other properties of these shapes as well.

Some special kinds of triangles are shown below; the right-angled triangle, isosceles triangle, and equilateral triangle. Sides that are the same length are marked with the same symbol, usually a short line, perpendicular to the side.

A triangle in which all the sides have different lengths is known as a scalene triangle. Some examples are shown below. You will see that a right-angled triangle can also be described as a scalene triangle.

Another important fact is that the angles of a triangle add up to 180º. To illustrate this, if you cut out any triangle and then tear off the angles, you will be able to arrange them to form a straight line. Draw a triangle and have a go yourself.

Shapes that have four straight edges are known as quadrilaterals. Squares and rectangles are special kinds of quadrilaterals.

A quadrilateral that has one set of parallel sides is known as a trapezoid.

If the quadrilateral has two sets of parallel sides, it is called a parallelogram.

When you are describing a geometrical figure, you often need to refer to a particular line or angle on the diagram. This can be done by labeling the diagram with letters. For example, the diagram below shows a triangle ABC, in which the longest side is AB and the angle cap a times cap c hat times cap b is a right angle. cap a times cap c hat times cap b is the angle formed by the lines AC and CB. The point where two lines meet is known as a vertex (the plural is vertices). So A, B, and C are vertices of the triangle.

Note that you can use the shorthand notation “ prefix white up pointing triangle of cap a times cap b times cap c” for “the triangle ABC” if you wish. You may have come across a lot of new math vocabulary in this section—remember to include any in your math notebook.

10.4.2 What Can You See?