1. The Pythagorean Theorem
Lesson 7-1
The Pythagorean Theorem
Lesson 7-1: The Pythagorean Theorem

2. The Pythagorean Theorem
Given any right triangle, A2 + B2 = C2 C A B
Lesson 7-1: The Pythagorean Theorem

3. Lesson 7-1: The Pythagorean Theorem
Example
In the following figure if A = 3 and B = 4, Find C.
A2 + B2 = C2
= C 2
= C2
5 = C C A B
Lesson 7-1: The Pythagorean Theorem

4. You can verify 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.
Lesson 7-1: The Pythagorean Theorem

5. Pythagorean Theorem : Examples
C = 17
A=8, B= 15, Find C
A=7, B= 24, Find C
A=9, B= 40, Find C
A=10, B=24, Find C
A =6, B=8, Find C
C = 25 C A
C = 41
C = 26 B
C = 10
Lesson 7-1: The Pythagorean Theorem

6. Finding the legs of a right triangle:
In the following figure if B = 5 and C = 13, Find A.
A2 + B2 = C2
A = 132
A = 169
A =169-25
A2 = A = 12 C A B
Lesson 7-1: The Pythagorean Theorem

7. Lesson 7-1: The Pythagorean Theorem
More Examples:
B = 6
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
B = 8
A = 24
C = 25 C
B = 10.6 A
A = 8.7
C = 10
B = 17.9 B
Lesson 7-1: The Pythagorean Theorem

8. Lesson 7-1: The Pythagorean Theorem
Given the lengths of three sides, how do you know if you have a right triangle?
Given A = 6, B=8, and C=10, describe the triangle.
A2 + B2 = C2
= 102
= 100
This is true, so you have a right triangle. C A B
Lesson 7-1: The Pythagorean Theorem

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
Lesson 7-1: The Pythagorean Theorem

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
Lesson 7-1: The Pythagorean Theorem

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=14
6) A=2, B=3, C=4
7) A=1, B=7, C=7
8) A=90, B=120, C=150
right
right
obtuse
right C
acute A
obtuse
acute
right B
Lesson 7-1: The Pythagorean Theorem