The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It can be written as a2 + b2 = c2, where c is the hypotenuse and a and b are the other two sides. The theorem can be used to calculate unknown sides of right triangles and determine if a triangle is a right triangle. It has various applications in fields like engineering and construction. Examples are provided to demonstrate using the theorem to solve problems and prove the relationship between the sides of a right triangle.

1. The Pythagorean Theorem
XUNJIA TIAN
EDCI 335 ASSIGNMENT2

2. Who wants to be a millionaire?
A video, contestant who wants to be a millionaire lost $15,000, because
he didn’t know the Pythagorean Theorem.
https://www.youtube.com/watch?v=BbX44YSsQ2I

3. What is the Pythagorean Theorem?

4. What you need to know?
Right triangle:
A right triangle is a triangle with angle of 90 degree.
Hypotenuse :
The longest length in the right triangle, labeled as letter “c”
90 degree
c

5. Definition:
In a right triangle, the square of the hypotenuse is equal to the
sum of the square of the other two sides. The Pythagorean
Theorem can be written as an equation a2+b2=c2.
c
b
a

6. Application in real world
Civil Engineer:
Bridge building

7. Building a Slide Park
Application in real world

8. Building house roof
Application in real world

9. Prove the Pythagorean Theorem
Video shows several ways
https://www.youtube.com/watch?time_continue=16&
v=_87RbSoELW8

10. Activity:
Prove the Pythagorean Theorem by yourself
Material needed:
paper, pen and scissor
Steps:
1. Draw a right triangle on the paper
2. Draw a square along the hypotenuse
3. Draw the same sized square on the other two sides.
4. Draw lines as shown on the video.
5. Cut out the shapes
6. Arrange them so that you can prove that the big square has the same
area as the two squares on the other sides

11. c2
a2
b2
c2
b2 + a2
Two squares have same area.

12. Practice 1:
Question 1: Solve this triangle
5
c
12
Solution:
1. start with a2 + b2=c2
2. put in what we know 52 + 122=c2
3. calculate squares: 25+144=169=c2
4. swap sides: c2 = 169
5. square roots of both sides: c= √169
4. calculate : c= 13

13. Practice 2:
Question 2: Solve this triangle
9
15
b
Solution:
1. start with a2 + b2=c2
2. put in what we know 92 + b2=152
3. calculate squares: 81+b2=225
4. take 81 from both sides: 81+ b2 -81 = 225-81
5. calculate : b2= 144
7. calculate : b= 12
6. square root of both side : b= √144

14. Practice 3:
Question 3: what is the diagonal distance across a square of size 1?
1 1
1
Solution:
1. start with a2 + b2=c2
2. put in what we know 12 + 12=c2
3. calculate squares: 1+1=2=c2
4. swap sides: c2 = 2
5. square roots of both sides: c= √2
4. c= 1.1412
1
?

15. Practice 4:
Question 1: Does an 8,15 ,16 triangle have a right angle ?
8
16?
15
Solution:
1. Does 82 + 152=162 ??
2. 82 + 152= 64 +225 =289
but 162=256
So, No. it does not have a right triangle.

16. Summary :
• Pythagorean Theorem can be used only for right triangle.
• In a right triangle, the sum of two short sides must be
greater than the hypotenuse.
• The square of the hypotenuse is equal to the sum of
square of other two sides.

17. Conclusion :
Here is an extra video presenting lesson.
https://www.youtube.com/watch?v=WqhlG3Vakw8
Don’t forget assignment!!!

18. Reference :
pictures:
http://www.perkinselearning.org/activity/practical-application-pythagorean-theorem-
building-slide-park
https://simon.sjcmda.vic.edu.au/TLFLearningObjects/DVD/los/L6559/index2.html
https://www.futura-sciences.com/sciences/personnalites/mathematiques-pythagore-
samos-204/
http://farhek.com/jd/u41374k0/right-students/10ck473/
https://www.google.ca/search?hl=en-
CA&biw=1440&bih=839&tbm=isch&sa=1&ei=wOI2W7WkCuCQ0PEPpaKY2AU&q=math
&oq=math&gs_l=img.3..35i39k1l2j0i67k1l6j0l2.95152.97465.0.97902.35.16.0.0.0.0.75.
832.14.14.0....0...1c.1.64.img..29.6.401.0..0i30k1.0.hqTEE0XKdo8#imgrc=GTDOOaxAfZg
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