Print this chapterPrint this chapter

Module 6

1. Module 6

1.27. Page 2

Mathematics 10-3 Module 5 Introduction

Module 6: Triangles and Other Polygons

 

Get Started

 

In this activity you will examine a method of drawing a triangle if given the lengths of its three sides.

 

Try This

 

Work with a partner, if possible. Complete this construction as outlined below.

 

Suppose you were asked to construct a triangle with sides 13 cm, 12 cm, and 5 cm.

 

Step 1: With your ruler, draw a line segment, 13 cm long. You could also have drawn the segment 12 cm or 5 cm long but, generally, it is easier in subsequent steps if you choose the longest side.

 

This illustration shows a line segment labelled AB measuring 13 centimetres.

 

Step 2: Open your compass to a radius of 12 cm. Note: You could use 5 cm in this step but, again, to simplify the procedure, the longer of the two remaining sides is chosen. With centre A and the radius of 12 cm, draw an arc where you judge the third vertex of the triangle to be.

 

This illustration shows a line segment measuring 13 centimetres and labelled AB. An arc with a radius of 12 centimetres is drawn from point A.

 

Step 3: Open your compass to a radius of 5 cm. With centre B and the radius of 5 cm, draw an arc intersecting the first arc. Call this point C.

 

This illustration shows segment AB. It measures 13 centimetres in length with an arc of radius 12 centimetres centred at point A and an arc of radius 5 centimetres centred at B.

 

Step 4: Join A, B, and C.

 

This illustration shows triangle ABC with side AB measuring 13 centimetres. Side BC measures 5 centimetres. Side AC measures 12 centimetres. Also shown are arcs. There is an arc of radius 12 centimetres centred at point A and an arc of radius 5 centimetres centred at B. These arcs intersect at vertex C of the triangle.

 

Now answer the following questions.

 

Self-Check

 

SC 1. The angle at C looks like it is a right angle. Use your protractor to measure What is its measure?

 

SC 2. Suppose you didn’t have a protractor. How could you prove that is a right angle? Show your steps.

 

SC 3. What is the term for the three numbers 5, 12, and 13 that proves is a right triangle?

 

Compare your answers.