1. Ch 11.3 – The Pythagorean Theorem
MJ2
Ch 11.3 – The Pythagorean Theorem

2. Bellwork Solve 72 + 52 =c 42 + b = 36 32 + a = 25 92 + 22 = c
Solutions 74 20 16 85

3. Assignment Review
Text p. 477 # 13 – 28

4. Before we begin Please take out your notebook and get ready to work…
In the last couple of lessons we worked with squares & square roots…
In today’s lesson we will apply what we learned about squares and square roots to finding the side of a right triangle using the Pythagorean theorem

5. Objective 11.3
Students will find the length using the Pythagorean theorem.

6. Background Information
Pythagoras was a Greek mathematician and philosopher who lived in ancient times…
he studied the world around him and made an observation that applies to all right triangles…
That is…there is a relationship between the legs of a right triangle and the hypotenuse.

7. Vocabulary
Before we can work with the Pythagorean theorem there are some terms you need to know:
Right triangle – a triangle with a 90° angle
Legs – the 2 shorter sides of a right triangle
Hypotenuse – the longest side of a right triangle. The hypotenuse is always opposite the right angle

8. Parts of a Right Triangle
In the notes section of your notebook draw and label the right triangle
hypotenuse
Right angle symbol
Legs

9. Pythagorean Theorem a2 + b2 = c2
The Pythagorean theorem can be expressed as an algebraic equation as follows:
a2 + b2 = c2
Where a and b represent the legs
Where c represents the hypotenuse

10. Working with the Pythagorean Theorem
When working with the Pythagorean theorem you will use the formula method.
Write the formula
Substitute
Do the math
The formula method minimizes errors and demonstrates what you know…
I will not accept any work that does not show the formula method!

11. Example To find the length of c a2 + b2 = c2 152 + 82 = c2
1. Write the formula
2. Substitute
3. Do the math
15 ft
8 ft c
17 = c
Solution

12. Comments
Your ability to be organized here will enable you to be successful!
It doesn’t matter which leg you call a or b.
It does matter that the hypotenuse (c) is on the other side of the equals sign
You name the given parts and substitute them under where they belong in the formula
Again, you are required to demonstrate what you know!

13. Your Turn
In the notes section of your notebook draw & label the triangle and find the missing measurement using the Pythagorean theorem b
5 cm
16 cm
4 cm x
9.2 cm

14. Your Turn Solution #1 52 + b2 = 162 25 + b2 = 256 -25 -25 b2 = 231
a2 + b2 = c2 b
5 cm
16 cm
52 + b2 = 162
25 + b2 = 256
b2 = 231
b = 15.1 cm

15. Your Turn Solution #2 a2 + 42 = 9.22 a2 + 16 = 84.64 -16 -16
a2 + b2 = c2
4 cm x
9.2 cm
a = 9.22
a =
a =
a = 8.3 cm

16. Summary
In the notes section of your notebook summarize the key concepts covered in today’s lesson
Today we discussed:
The Pythagorean theorem – what is it and what do you apply it to?

17. Assignment Text p. 482 # 9 – 16 Reminder
This assignment is due tomorrow
I do not accept late assignments
You must draw the picture and use the formula method to show how you got your answer
I will not accept answers only for a grade