Module 6

1. Module 6

1.2. Page 2

Mathematics 10-3 Module 6 Lesson 1

Module 6: Triangles and Other Polygons

Get Started

This illustration shows a cartoon figure of a cow.

In this next activity you will draw a favourite cartoon character. Your final drawing will be larger than the original but geometrically similar in shape.

The activity is described using a cartoon of a happy cow; however, you may search the Internet or magazines for a cartoon character or art design you prefer to enlarge.

Try This

Work with a partner, if possible.

Step 1: Locate or print out a small cartoon character or art design that you wish to enlarge. You may use the Happy Cow image or you may choose another image. Cut around the figure and recycle the waste.

This illustration shows a cow cartoon figure with one eighth-inch grid overlaying it. An extra row of squares is placed above the image, and an extra column of squares is placed to the left of the image. The top row has the letters A through J placed from left to right in the squares. The left column has the numbers 1 through 10 placed in the squares from top to bottom.

Step 2: Download one sheet each of Eighth-Inch Grid Paper, Quarter-Inch Grid Paper, and Half-Inch Grid Paper. Paste the figure on the eighth-inch grid paper, and extend the grid lines over the cartoon figure, as in the example. As in the example, label the grid to identify each square of the figure to be enlarged.

Step 3: Label the quarter-inch and the half-inch grid paper the same way you did for the eighth-inch grid. In each square, draw what you see. In square A3, you would draw what you see on the figure.

This is a sample of what you see in A3 on the eighth-inch grid.

This is a sample of what you draw in A3 on the quarter-inch grid.

This is a sample of what you draw in A3 on the half-inch grid.

When you are done, you will have two enlargements. The following is the half-inch grid enlargement of the happy cow.

This illustration shows a cow cartoon figure with a half-inch grid overlaying it. An extra row of squares is placed above the image, and an extra column of squares is placed to the left of the image. The top row has the letters A through J placed from left to right in the squares. The left column has the numbers 1 through 10 placed in the squares from top to bottom.

When you have completed your enlargements, answer the Self-Check questions. Save your answers in your course folder.

scale factor: the number by which the length and the width of a figure are multiplied to form a larger or smaller similar figure

Recall that the number of times the length and the width is increased or decreased is called the scale factor. If both the length and the width are tripled in size, the scale factor is three.

Self-Check

SC 1. What is the scale factor by which the length and the width were increased from the original figure on the eighth-inch grid to your first enlargement on the quarter-inch grid? How do you know?

SC 2. How many times larger in area is the enlargement on the quarter-inch grid than the original on the eighth-inch grid? How do you know?

SC 3. What is the scale factor by which the length and the width were increased from the original figure on the eighth-inch grid to your second enlargement on the half-inch grid? How do you know?

SC 4. How many times larger in area is the enlargement on the half-inch grid than the original on the eighth-inch grid? How do you know?

SC 5. Suggest how you could reduce an image to one-half its length and one-half its width?

Compare your answers.

The figures on the three sizes of grid paper are similar figures, geometrically speaking.

In the following activity, you are going to investigate similar polygons.

similar figures: figures with the same shape but not necessarily the same size

A figure similar to another may be larger or smaller than the other.

polygon: a many-sided figure

A triangle is a polygon with three sides, a quadrilateral is a polygon with four sides, and so on.