Discovering Special Right Triangle Rules
Use the Pythagorean Theorem to find the missing lengths in the following
45-45-90 (Isosceles right) triangles. Then complete the table below.
Be sure to give your answers in simplified radical form.
1.
2.
45
3
3.
5 2
5
8
3
45
45
8
4.
7 2
5.
45
12
7 2
Triangle #
1
2
3
4
5
Leg
45
Leg
Look for patterns in the numbers.
Can you come up a rule for the hypotenuse based on the leg?
Can you come up with a rule for one leg based on the other?
Hypotenuse
Using your rules, can you complete the table below?
Triangle #
6
7
8
9
10
11
Leg
13
Leg
Hypotenuse
5
15√2
9
7√2
8√2
Can you continue to follow the patterns on more difficult questions…
Find the missing lengths for each triangle. Be sure to give your answers in
simplified radical form.
12.
13.
16
3
45
14.
15.
45
45
11
8 2
16.
45
3 6
Use the Pythagorean Theorem to find the missing lengths in the following
30-60-90 Triangles.
17.
18.
7 3
19.
30
5 3
4
10
7
60
60
20.
21.
30
11 3
2
18
9
22
30
Use the Pythagorean Theorem to find the missing side if each triangle. Then
complete the table below. Be sure to give your answer in simplified radical form.
Triangle #
17
18
19
20
21
Short leg
Long leg
Hypotenuse
Look for patterns in the numbers.
Can you come up a rule for the hypotenuse based on the short leg?
Can you come up with a rule for the long leg based on the short leg?
Using your rules, can you complete the table below?
Triangle #
22
23
24
25
26
27
Short leg
13
Long Leg
Hypotenuse
10√3
32
20
3√3
6
Can you continue to follow the patterns on more difficult questions…
Find the missing lengths for each triangle. Be sure to give your answers in
simplified radical form.
6
28.
30
29.
3 3
30
30.
31.
4
5 6
60
32.
30
16 3
60