1. Module 6

1.30. Page 5

Mathematics 10-3 Module 5 Introduction

Module 6: Triangles and Other Polygons

 

Lesson Summary

 

Fractal art is based on similarity. The “trees” in the illustrations were created by drawing similar Pythagorean relationships on progressively smaller scales. As you can see, each square on the legs of a right triangle becomes the square on the hypotenuse of a smaller but similar right triangle, and so on, and so on!

 

This is a fractal image of the Pythagoras tree.

 

You can see how these trees were created in the applet “Grand Pythagorean Tree” To make the tree grow, press “More.” To start over, press “Reset.” For a variety of trees, adjust the “Slant” slider.

 

The Pythagoras tree is just one of many applications of the Pythagorean Theorem.

In this lesson you explored the following question:

  • How is the Pythagorean Theorem applied to solve a variety of practical problem situations?

Check your level of understanding of the materials covered in this lesson by completing “Lesson 6 Traffic Lights.” If you select an amber or red traffic light in the multimedia piece, you will receive information about additional work you can complete to improve your understanding of the topics. Complete the suggested work before you proceed to the Lesson 6 Assignment. If you experience difficulty, contact your teacher before starting the Lesson 6 Assignment.

 

In this lesson you used the Pythagorean Theorem in various situations to find the missing side of a right triangle from the other two sides. You also applied the Pythagorean Theorem to check if the lengths of three sides could form a right triangle. In every case, you applied the fact that the area of the square constructed on the longest side of a right triangle equals the sum of the areas of the squares on the two remaining sides.

 

m10_3_assign.jpg Assignment

 

Retrieve the Lesson 6 Assignment Booklet you saved in your course folder at the start of this lesson. Complete the Assignment Booklet. Resave your Assignment Booklet in your course folder and submit a copy to your teacher for assessment.

 

Unit 3 Project

 

In Lesson 3 of this unit, you were asked to identify similar triangles in your Unit 3 Project topic. Were any of those triangles right triangles? Would using the Pythagorean theorem help you to identify whether they are right triangles? Could the theorem help you find the length of one of the sides in a right triangle?

 

Take some time to explore the possible connections between your topic and the Pythagorean Theorem. Save any sketches and calculations in your course folder for use in your project presentation. For more information about this step and later steps of the Unit 3 Project, refer to the Unit 3 Project.