Name ____________________________________
Right Triangle Practice
Date _________________
Pythagorean Triples
A Pythagorean Triple is a set of three counting numbers that are the lengths of the sides of a right triangle.
10
5
3
6
15
9
4
8
12
The triangles above are all members of the (3, 4, 5) family.
For example, the triple (6, 8, 10) is ( 3• 2, 4 • 2, 5 • 2 ) .
Other common families are:
(5, 12, 13)
(7, 24, 25)
(8, 15, 17)
Problems: Find the missing side in each triangle:
1. (3, 4, 5)
x
20
15
2. (5, 12, 13)
26
24
x
(9, 40, 41)
(11, 60, 61)
45°
n 2
n
€
45°
n
Problems: Find the missing lengths in each triangle.
1.
A
AB = __________
9
45°
BC = __________
45°
C
B
2.
D
DE = __________
45°
7 2
FE = __________
45°
€
E
F
3.
H
GI = __________
45°
3
HI = __________
45°
I
G
4.
5.
x
x
45°
45°
15
9
6. You are looking at a series of isosceles right triangles. AB = 1.
B
A
Find:
D
C
AC = ________! !
BC = ________
CD = ________! !
CE = ________
BD = ________! !
DE = ________
EF = ________! !
DF = ________
E
F
7. Given ABCD is a square with BD = 10 2 . How long is a side of the square?
B
C
€
A
D
8.
R
RS = 16 2
45°
RM = ________
€
45°
S
M
60°
2n
n
30°
n 3
Problems:
€
1. AC = ________
2. AB = ________
BC = ________
BC = ________
A
8
A
60°
60°
8
30°
30°
B
C
3. AC = _________
B
C
4. AC = ________
AB = ________
AB = ________
A
A
60°
60°
30°
30°
B
8 3
€
C
B
8
C
5. AT = ________
6. DG = ________
CT = ________
OG = ________
C
G
6
D
A
30°
60°
5
T
O
7. BC = ________
8. EG = ________
AB = ________
FG = ________
B
12
E
60°
30°
A
5 3
€
C
G
F
Mixed Problems: Find x:
1.
2.
3
5
10
8
x
x
3.
4.
45°
x
x
2
5 2
45°
€
5.
6.
x
60°
11
12
30°
x
7.
8.
x
x
3 2
30°
€
9