Download Vocabulary - Hartland High School

Section 5.5 Use Inequalities in a Triangle
Goal  Find possible side lengths of a triangle.
Sides and Angles Theorem
The longest side of a triangle corresponds to the
largest angle. The smallest side of a triangle
corresponds to the smallest angle.
Sides and Angles Converse Theorem
The largest angle of a triangle corresponds to the
largest side. The smallest angle of a triangle
corresponds to the smallest side.
E
B
18
FE < ED < FD
D < F < E
22
F
25
105
A
C < A < B
AB < BC < AC
60
15
D
C
Example 1: Write the measurements of the triangle in order from least to greatest.
a.
b.
Checkpoint: Write the measurements of the triangle in order from least to greatest.
1.
2.
Example 2: A triangle has sides that are 33, 18, and 24 centimeters long and angles of about 32°,
103°, and 45°. Sketch and label a diagram with the shortest side on the bottom and the largest angle at
the left.
Checkpoint:
3. A right triangle has sides that are 16, 34, and 30 inches long and angles of 90°, about 28°, and about
62°. Sketch and label a diagram with the shortest side on the bottom and the right angle at the left.
Section 5.5 Use Inequalities in a Triangle
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
NO + OP > NP
OP + NP > NO
NP + NO > OP
O
N
P
Example 3: Is it possible to construct a triangle with the given side lengths? If not, explain why not.
a. 5, 6, 10
b. 4, 5, 9
Example 4: A triangle has one side of length 14 and another of length 10. Describe the possible
lengths of the third side.
Checkpoint: Two sides of a triangle are given. Describe the possible lengths of the third side.
4. 2 centimeters and 5 centimeters