# Easy Triangle Inequalities ```Worksheet Triangle Inequalities
Name ___________________
Decide whether each set of numbers is a triangle.
1) 15, 12, 9
2) 23, 16, 7
3) 20, 10, 9
4) 8.5, 6.5, 13.5
5) 47, 28, 70
6) 28, 41, 13
7) 5, 10, 15
8) 9, 40, 41
9) 12, 2.2, 14.3
10) 6,9, 16
The measures of two sides are given. Between what two numbers must the third side fall.
11) 9 and 15
12) 11 and 20
13) 23 and 14
14) 5 and 8
15) 15 and 18
16) 22 and 34
17) 47 and 71
18) 21 and 47
Name the largest and the smallest angle.
19)
20)
C
6
5
A
F
5
7
B
D
21)
5
J
3
5.1
5.03
4
E
List the angles of ∆ ABC from the smallest to the largest.
22) AB = 17, BC = 21, AC = 18
H
23) AB = 15, AC = 16, BC = 17
G
List the sides in order, underline the side with the shortest length.
24)
25)
A
63&deg;
B
70&deg;
47&deg;
30&deg;
E
C
125&deg;
B
26)
D
25&deg;
F
A
65&deg;
40&deg;
List the sides of ∆ ABC from the longest to shortest.
27) m ∠A = 46&deg;, m ∠B = 30&deg;
28) m ∠C = 101&deg;, m ∠B = 70&deg;
29) m ∠A = 59&deg;, m ∠C = 61&deg;
Find the value of x and list the sides of ∆ ABC in order from shortest to longest if the angles have the
indicated measures. (Hint: Find the angle measures first, then decide which sides are the longest)
30) m ∠A = ( 9x + 29 ) &deg; , m ∠B = ( 93 − 5x ) &deg; ,
31) m ∠A = ( 9x − 4 ) &deg; , m ∠B = ( 4 x − 16 ) &deg; ,
and m ∠C = ( 68 − 2x ) &deg; .
32) m ∠A = (12x − 9 ) &deg; , m ∠B = ( 62 − 3x ) &deg; ,
33) m ∠A = ( 5x + 2 ) &deg; , m ∠B = ( 6x − 10 ) &deg; ,
34) m ∠A = (10 x ) &deg; , m ∠B = ( 5x − 17 ) &deg; ,
and m ∠C = (10 x + 2 ) &deg; .
and m ∠C = (16 x + 2 ) &deg; .
and m ∠C = ( x + 20 ) &deg; .
and m ∠C = ( 7x − 1) &deg; .
35) Draw
∆DEA with a median EG .
37) Find the value of x.
SO is an altitude of ∆SAT
S
( 4x
T
O
− 6)&deg;
A
36) Draw ∆JKH with an altitude JP .
C
```