Canadian Grade 8 Curriculum - Pythagorean Theorem

1. Objective- To solve problems involving
the Pythagorean Theorem.
For Right Triangles Only!
leg
hypotenuse - always opposite
leg
the right angle

2. For Right Triangles Only!
leg
hypotenuse
c
leg
a
b

3. ba
ab
hypotenuse c

4. Objective- To solve problems involving
a
the Pythagorean Theorem.
For Right Triangles Only!
c a2 + b2 = c2
b
Pythagorean Theorem

5. 6
x
8
a2 + b2 = c2
62 +82 = x2
36 + 64 = x2
100 = x2
100 = x2
10 = x
x =10 or -10
Solve for x.

6. 4
7
y
a2 + b2 = c2
Solve for y.
72 + 42 = y2
49 +16 = y2
65 = y2
65 = y2
y = 65 or - 65
y » 8.1
a
b c

7. 6
t
15
a2 + b2 = c2
Solve for t.
t2 + 62 =152
t2 + 36 = 225
-36 -36
t2 =189
t2 = 189
t = 189
t »13.7

8. Pythagorean Triples
3 4 5
6 8 10
9 12 15
12 16 20

9. Pythagorean Triples
3 4 5
6 8 10
9 12 15
12 16 20
5 12 13
10 24 26
15 36 39
7 24 25
14 48 50
21 72 75
9
12
15

10. To the nearest tenth of a foot, find the length
of the diagonal of a rectangle with a width of
4 metres and a length of 10 metres.
4 m
10 m
a2 + b2 = c2
42 +102 = x2
16 +100 = x2
116 = x2
116 = x2
x = 116
x
x »10.8

11. A car drives 20 km due east and then 45 km
due south. To the nearest hundredth of a km,
how far is the car from its starting point?
20 miles
x 45 miles
a2 + b2 = c2
202 + 452 = x2
400 + 2025 = x2
2425 = x2
2425 = x2
x = 2425
x » 49.24

12. Proof
11/11/14 12

13. Informal Proof #1
Inscribe a square within the square.

14. Informal Proof #1
Yellow region = c2
a b
b c
a
a
a
b
c
b
c
c
c2

15. Informal Proof #1
Yellow region = c2
a b
b c
a
a
a
b
c
b
c
c
a
b c
c2

16. Informal Proof #1
b
Yellow region = c2
a
a
a
b
c
b
c
c
a
b c
c2

17. b
a
a
a
b
c
b
c
c
a
b c
c2
c b
a
Informal Proof #1
Yellow region = c2

18. b
a
a
c
b
c
a
b c
c2
c b
a
Informal Proof #1
Yellow region = c2

19. b
a
a
c
b
c
a
b c
c2
c b
a
b
c a
Informal Proof #1
Yellow region = c2

20. a
c
b
a
b c
c2
c b
a
b
c a
Informal Proof #1
Yellow region = c2

21. a
c
b
a
b c
c2
c b
a
b
c a
a
c
b
Informal Proof #1
Yellow region = c2

22. a
b c
c2
c b
a
b
c a
a
c
b
Informal Proof #1
Yellow region = c2

23. a
b c
c b
a
b
c a
a
c
b
Informal Proof #1
Yellow region = c2

24. a
b c
c b
a
b
c a
a
c
b
Informal Proof #1
Yellow region = c2
a
b c

25. c b
a
b
c a
a
c
b
Informal Proof #1
Yellow region = c2
a
b c
c b
a

26. b
c a
a
c
b
Informal Proof #1
Yellow region = c2
a
b c
c b
a
a
c
b

27. b
c a
Informal Proof #1
a
b c
c b
a
a
c
b
b
c a
Yellow region = c2

28. Informal Proof #1
Yellow region = c2
a
b c
c b
a
a
b2
c
b
b
c a
a2
Yellow region = a2 + b2
a2 + b2 = c2

29. Informal Proof #2
a + b Total Purple Yellow
a b
b c
a
a
a
b
c
b
c
c
c2
Area - Area = Area
(a + b)2- 4 1 ab
æ ö
çè 2
÷ø
= c2
a2 + 2ab + b2 -2ab = c2
a2 + b2 = c2