Pythagorean Triples

1
Pythagorean Triples

• Beat the Computer Drill

2
What are Pythagorean Triples?

• Three integers that make the equation a2 b2
  c2 true are called Pythagorean Triples.
• The numbers 3, 4 and 5 are a very famous
  Pythagorean Triple.

a2 b2 c2
32 42 52
9 16 25
3
Why Memorize Pythagorean Triples?

• Remember how much time it took to figure out 8 x
  8 before you memorized it?
• (8 8 8 8 8 8 8 8 64)
• Think of all the work involved to solve this
  problem

Wouldnt it be nice to just know this is 5?
a2 b2 c2
32 42 x2
9 16 x2
25 x2
5 x
4
Good Pythagorean Triples to Memorize
And multiples of each, like 3x2, 4x2, 5x2 6
8 10
5
Directions

• The following slides show common Pythagorean
  Triples. It is faster to recognize these triples
  on sight than to apply the Pythagorean Theorem.
• When the right triangle appears, SAY ALOUD
  the length of the missing side. Try to beat the
  computer by saying the answer BEFORE it appears
  in 8 seconds.

6
4
x
3
7
4
3
5
4
5
3
8
12
x
5
9
12
5
13
12
13
5
10
10
8
x
11
8
10
6
12
50
x
30
13
4
3
5
x 10
x 10
x 10
40
30
50
50
40
30
14
5
x
3
15
4
3
5
5
4
3
16
12
13
x
17
12
5
13
12
13
5
18
24
x
18
19
4
3
5
x 6
x 6
x 6
24
18
30
24
30
18
20
x
8
15
21
15
8
17
17
8
15
22
0.5
x
0.3
23
4
3
5
x .1
x .1
x .1
0.4
0.3
0.5
0.4
0.5
0.3
24
36
x
27
25
4
3
5
x 9
x 9
x 9
36
27
45
36
45
27
26
13
x
5
27
12
5
13
13
12
5
28
20
25
x
29
4
3
5
x 5
x 5
x 5
20
15
25
20
25
15
30
17
8
x
31
15
8
17
17
8
15
32
40
x
24
33
4
3
5
x 8
x 8
x 8
32
24
40
40
32
24
34
5
4
x
35
4
3
5
5
4
3
36
15
x
9
37
4
3
5
x 3
x 3
x 3
16
9
15
12
15
9
38
17
x
15
39
15
8
17
17
8
15
40
28
35
x
41
4
3
5
x 7
x 7
x 7
28
21
35
28
35
21
42
16
x
12
43
4
3
5
x 4
x 4
x 4
16
12
20
16
20
12
44
Way to Go!!