Module 6
1. Module 6
1.28. Page 3
Module 6: Triangles and Other Polygons
Explore
In the Get Started section you examined how to draw a triangle if given the lengths of its sides. In the next activity you will explore further how the Pythagorean Theorem is used to determine whether or not a triangle is a right triangle given the lengths of its sides.
Try This
Work with a partner, if possible.
Follow these steps to complete the table in TT 1.
Step 1: Use the method outlined in Get Started to draw the triangles in the table. It will probably be easier to draw the sides, a, b, and c, in centimetres rather than in inches. However, any unit would do.
Step 2: After you draw each triangle, estimate, measure, and record the size of 
Round angle measures to the nearest degree.
Step 3: Complete each row of the table to see which values of a, b, and c form Pythagorean triples.
TT 1. Complete this table.
|
Triangle |
a |
b |
c |
a2 |
b2 |
c2 |
a2 + b2 |
Estimate ∠C |
Measured ∠C |
|
#1 |
3 |
4 |
5 |
|
|
|
|
|
|
|
#2 |
4 |
5 |
6 |
|
|
|
|
|
|
|
#3 |
5 |
6 |
7 |
|
|
|
|
|
|
|
#4 |
6 |
8 |
10 |
|
|
|
|
|
|
|
#5 |
8 |
15 |
17 |
|
|
|
|
|
|
|
#6 |
6 |
16 |
17 |
|
|
|
|
|
|
TT 2. How do you know that 
would be the right angle in these triangles? Why didn’t you measure 
or 
to see if they were the right angle in the triangle?
TT 3. Which triangles were right triangles? Why?
TT 4. Which values of a, b, and c form Pythagorean triples?
TT 5. Using the ratio 8, 15, 17, form four more sets of Pythagorean triples.
Share
Share and compare your answers to TT 1 to TT 5 with a partner or group. Place your final answers in your course folder.
Did anyone you shared with not draw the six triangles but still have data in her or his table and answers to the questions? How would it be possible to complete the previous Try This questions without ever drawing any triangles? How does having an image of the triangles help you?
Summarize your discussion and your responses to the Share questions in a short paragraph. Save this in your course folder.