1. THE PYTHAGOREAN THEOREM
An Introduction to Triangles

2. THE PYTHAGOREAN THEOREM
Given any Right Triangle, A2 + B2 = C2 C A B

3. How do you use the Pythagorean Theorem
Let A = 3 and B = 4
C2 = A2 + B2
C2 =
C2 =
C = 5 C A B

4. You can prove the Pythagorean Theorem with the following:
Given a piece of graph paper, make a right triangle. Then make squares of the right triangle. Then find the square’s areas.

5. Solve the problems below using the Pythagorean Theorem
1) A=8, B= 15, Find C
2) A=7, B= 24, Find C
3) A=9, B= 40, Find C
4) A=10, B=24, Find C
5) A =6, B=8, Find C
6) A =7, B=10, Find C
7) A =4, B =5, Find C
8) A=18, B=80, Find C C A B

6. How do you solve for A or B?
Let B = 5 and C = 13
A2 + B2 = C2
A = 132
A = 169
A =169-25
A2 = 144
A = 12 C A B

7. Solve the problems below using the Pythagorean Theorem
1) A=8, C =10 , Find B
2) A=15, C=17 , Find B
3) B =10, C=26 , Find A
4) A=15, B=20, Find C
5) A =12, C=16, Find B
6) B =5, C=10, Find A
7) A =6, B =8, Find C
8) A=11, C=21, Find B C A B

8. Given the lengths of three sides, how do you know if you have a right triangle?
Let A = 6, B=8, and C=10
A2 + B2 = C2
= 102
= 100
This is true, so you have a right triangle. C A B

9. If A2 + B2 > C2, you have an acute triangle.
Given A = 4, B = 5, and C =6, describe the triangle.
A2 + B2 = C2
= 62
= 36
41 > 36, so we have an acute triangle. A B C

10. If A2 + B2 < C2, you have an obtuse triangle.
Given A = 4, B = 6, and C =8, describe the triangle.
A2 + B2 = C2
= 82
= 64
52 < 64, so we have an obtuse triangle. A B C

11. Describe the following triangles as acute, right, or obtuse
1) A=9, B=40, C=41
2) A=10, B=15, C=20
3) A=2, B=5, C=6
4) A=12, B=16, C=20
5) A=11, B=12, C=20
6) A=2, B=3, C=4
7) A=1, B=7, C=7
8) A=90, B=120, C=150 C A B