1. Module 6

1.12. Page 2

Mathematics 10-3 Module 6 Lesson 3

Module 6: Triangles and Other Polygons

 

Get Started

 

In this activity you will review the relationships among the corresponding sides and angles of similar triangles.

 

Try This

 

Work with a partner, if possible.

 

TT 1. With your partner, identify at least three pairs of similar triangles in your surroundings.

 

Save your answer in your course folder, as you will be asked to copy your response into the Assignment Booklet later in the lesson.

 

TT 2. Consider the following two triangles.

 

This illustration shows two similar triangles. Triangle ABC on the left has angle A marked with a single arc, angle B marked with a double arc, and angle C marked with a four-pointed star. Side AB has a length of 6 units, AC has a length of 9 units, and side BC has a length of 12 units. Triangle DEF on the right has angle D marked with a single arc, angle E marked with a double arc, and angle F marked with a four-pointed star. Side DE has a length of 3 units, DF has a length of 4.5 units, and side EF has a length of 6 units.

 

The two triangles are similar. Write down the side ratios you could use to help prove the triangles are similar. What does the size of the ratio indicate about the two triangles?

 

TT 3. Take the side ratios you used in TT 2 and flip each fraction over. What do you notice about the new ratios? What does the size of the ratio tell you about the triangles?

 

Flipping Over

 

The previous example illustrates the important idea that flipping ratios can be used to help solve equations. The next example shows how useful flipping ratios can be.

 

Example 1

 

Solve

 

Solution

 

Many people prefer to see the variable in the numerator (on top of the fraction) rather than in the denominator, where the variable is in this case. Whenever you have a proportion (two equal ratios), you can flip the ratios in the equation.

 

So,

 

 

 

Check by substituting for x in the original equation. Check It works!

 

Self-Check

 

Practise this technique. Solve each equation.

 

SC 1.

 

 

SC 2.

 

 

SC 3.

 

 

Compare your answers.