1. Module 6

1.8. Page 3

Mathematics 10-3 Module 6 Lesson 2

Module 6: Triangles and Other Polygons

 

Explore

 

In the previous lesson you used grids and elastic bands to draw similar polygons. In this activity you will explore another method of sketching similar polygons. You will also review the relationships between similar polygons.

 

Try This

 

Step 1: Print the “Pivot Point and Triangle ABC” diagram.

 

This illustration shows triangle ABC at the right with a point labelled P at the left.

 

 

Step 2: You may be reminded of the approach with elastics. However, instead of using elastics, join point P to each vertex of the polygon as shown here.

 

This illustration shows triangle ABC in red with each vertex joined to point P with a blue line.

 

Step 3: Measure out halfway from P to A. Call this point Measure out halfway from P to B. Call this point Measure out halfway from P to C. Call this point Join these points to form

 

This illustration shows triangle ABC in red with each vertex connected to point P with a blue line. Point A' is marked at the midpoint of segment PA. Similarly B' and C' are marked on PB and PC, respectively. The points A', B', and C' form triangle A'B'C', which is drawn in green.

 

In the last lesson you learned two things that are true for all similar polygons. What are those truths?

 

TT 2. How can you prove that the two triangles you just drew are similar triangles? Record your work to prove your results.

 

Share

 

Share and compare your work from TT 2 with a partner or group. Take note of the similarities and differences between the ways used to prove the triangles are similar. Discuss the following questions and summarize your discussion in a paragraph.

  • Is there one method that will work in all cases?

  • Did any of the methods use a scale factor or ratios to prove the triangles are similar?

  • How could a scale factor or ratio indicate the size of the similar polygon?

Save a copy of your summary paragraph in your course folder.

The corresponding angles are congruent and corresponding side lengths are proportional; that is, the ratios are equal.