Triangle Inequality Theorem1 (Ss Aa)
◦ If one side of a triangle is longer than a second side, then the angle
opposite the first side is larger than the angle opposite the second side
Example 1. Name the smallest angle and the largest angle of the following triangle
15
E S
Y
16
17
Smallest Angle:
Largest Angle:
5.
Triangle Inequality Theorem1 (Ss Aa)
Example 2. Name the smallest angle and the largest angle of the following
triangle.
19
R
T
Y
18
24
Smallest Angle:
Largest Angle:
6.
Triangle Inequality Theorem2 (Aa Ss)
•If one angle of a triangle is larger than the second angle, then the side
opposite the first angle is longer than the side opposite the second angle.
Example 3. Name the shortest and longest side of the following triangle.
45⁰
N W
E
65⁰
70⁰ Shortest side:
Longest side:
7.
Triangle Inequality Theorem2 (Aa Ss)
Example 4.
Y O
J
Triangle Sum Theorem
Shortest side:
Longest side:
36⁰
54⁰
90⁰
8.
Triangle Inequality theorem3 ()
The sum of the length of any two side of a triangle is greater than the length of
the third side.
9.
Triangle Inequality theorem3 ()
Example 5.
9cm
5cm
10cm
Solution:
True
True
True
Thus, lengths of all the sides satisfy the triangle
inequality theorem.
10.
Triangle Inequality theorem3 ()
Example 6.
State if the three numbers can be measures of three sides of a triangle.
a. 2,3 and 6 b. 4,5, and 7
Solution:
False
True
True
Solution:
True
True
True
11.
Activity 1.
1. Findthe smallest angle and the largest angle of the following triangle.
(Theorem 1).
E
N
D
5 13
12
12.
Activity 1.
2. Findthe shortest and longest side of the following triangle
R
S
T
50⁰
70⁰
60⁰
13.
Activity 1.
3. Determineif the given length of segment can be the sides of a
triangle. 6cm, 11cm and 10cm.
14.
Instruction: Identify thesmallest and largest angle, and shortest and
longest side
1. 2.
P
E
T
13
12
11
F
R
Y
105⁰
46⁰
29⁰
15.
3. Determine whethera triangle with side lengths 5 units, 3
units, and 10 units satisfies the Triangle Inequality Theorem.
Show your solution.
