1. The Pythagorean Theorem
Pythagoras
a + b = c 2 2 2

2. Pythagorean Theorem Leg Leg Hypotenuse
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse
Hypotenuse
Leg
Leg

3. 25 C 2 2 5 2 A 2 3 9 2 4 2 B 16

4. 2 5 2 4 2 3 C 2 A 2 B 2 9 16 25

5. a c b Pythagorean Theorem Leg Leg Hypotenuse
Identify the sides of this right triangle a
Hypotenuse c
Leg b
Leg

6. a b c Pythagorean Theorem Leg Leg Hypotenuse
Identify the sides of this right triangle
Leg a b c
Leg
Hypotenuse

7. a b c Pythagorean Theorem 1 3 2
Identify the sides of this right triangle 3 a b c 1 2

8. c a b Pythagorean Theorem 1 3 2
Identify the sides of this right triangle 1 c 2 a b 3

9. Pythagorean Theorem a + b = c 5 + 7 = c 25 + 49 = c 74 = c 8.6 = c
Find the length of the missing side.
a + b = c 2 2 2 x
5 + 7 = c 2 2 2
= c 2
5 cm
74 = c 2
8.6 = c
7 cm

10. Pythagorean Theorem a + b = c 6 + 8 = c 36 + 64 = c 100 = c 10 = c
Find the length of the missing side.
a + b = c 2 2 2 x
6 + 8 = c 2 2 2
= c 2
6 cm
100 = c 2
10 = c
8 cm

11. Pythagorean Theorem a + b = c 3 + 5 = c 9 + 25 = c 34 = c 5.8 = c
Find the length of the missing side.
a + b = c 2 2 2 x
3 + 5 = c 2 2 2
= c 2
3 cm
34 = c 2
5.8 = c
5 cm

12. Pythagorean Theorem a + b = c 20 + 21 = c 400 + 441 = c 841 = c 29 = c
Find the length of the missing side.
a + b = c 2 2 2
= c 2 2 2
20 in
= c 2
841 = c 2
29 = c
21 in

13. a + b = c a + b = c a + 12 = 13 a + 144 = 169 a = 5 -144 -144 a = 25 2
12 cm
a = 169 2
-144
-144
13 cm
a = 25 2
a = 5

14. 17 in
15 in
Answer = 8 in

15. 24 in
25 in
Answer = 7 in

16. 11 10 9 8 7 x 6 6 x 8 5
Answer = 7.8 4
Answer = 8.9 3 5 2 4 1
-14
-13
-12
-11
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -1 -2 -3 7
Yellow = 7.8
Blue = 8.9
Green = 9.2
Purple = 7.3 -4 -5 -6
Answer = 9.2 6 -7 x 7 x
Answer = 7.3 -8 -9
-10 2
-11

17. 11 10 9 8 7 6 5 19 4 3 x 2 1
-14
-13
-12
-11
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 -1 -2 -3
X = 26.9 -4 -5 -6 -7 -8 -9 19
-10
-11

18. Pythagorean Theorem x Find the height of the building. 70 ft
(Round to the nearest ft)
70 ft x
Answer = 49 ft
50ft

19. Do not measure the desk directly.
Use the Pythagorean theorem to measure the height of the desk in centimeters.
Do not measure the desk directly.
Tape the end
of the fishing
line to the floor
2 meter fishing line
Measure this distance in cm

20. Converse of the Pythagorean Theorem
If the square of the length of one side of a triangle is equal to the sum of the squares of the length of the other two sides, then the triangle is a right triangle.
a + b = c 2 2 2
= 5 2 2 2
= 25
25 = 25

21. Identify a Right Triangle
The measure of three sides of a triangle are 5 inches, 12 inches, and 13 inches. Determine whether the triangle is a right triangle.
a + b = c 2 2 2 2 2
= 13 2
= 169
169 = 169

22. Identify a Right Triangle
The measure of three sides of a triangle are 8 inches, 10 inches, and 15 inches. Determine whether the triangle is a right triangle.
a + b = c 2 2 2 2 2
= 15 2
= 225
164 = 225

23. Identifying an Obtuse Triangle
If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse
a + b c 2 2
< 2 2 2
< 2
<
<

24. Identifying an Acute Triangle
If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, the triangle is acute.
a + b c
> 2 2 2
> 2 2 2
>
>

25. Pythagorean triple
Is a set of nonzero whole numbers a, b, and c that satisfy the equation a b = c 2 2 2
Here are some common Pythagorean triples
7,24,25
3,4,5
5,12,13
8,15,17