Section 5.5
Inequalities in One Triangle
OBJECTIVE:
To use inequalities involving angles and sides of
triangles
BIG IDEA:
Reasoning and Proof
ESSENTIAL UNDERSTANDINGS:
• The measures of the angles of a triangle are related to the lengths of the
opposite sides.
• The sum of the lengths of two sides of a triangle is related to the length of the
third side.
MATHEMATICAL PRACTICE: Make sense of problems and persevere in
solving them
THEOREMS
 If two _______________ of a triangle are not
_______________, then the _______________ angle
lies opposite the ____________________ side.
 If two _______________ of a triangle are not
_______________, then the _______________ side lies
opposite the _______________ angle
EXAMPLE
 EX 1: Write the measurements of the triangle in order from
least to greatest.
 a)
B
15
120
45
A
 c) G
b) D
7
C
F
d) A
13
E
15
30 B
72
39
I
H
C
50 D
THEOREMS
 Exterior Angle Inequality: The measure of an
_______________ angle of a triangle is ______________
than the measure of either of the two _________________
interior angles
 Triangle Inequality: The _______________ of the
_____________ of any __________ _______________
of a triangle is ____________________ than the length of
the _______________ side
EXAMPLE
 EX 2: Construct a triangle with the given side lengths, if
possible.
 a) 3 in., 3 in. and 8 in.
 b) 9 cm., 5 cm. and 11 cm
EXAMPLE
 EX 3: Two sides of a triangle are given. Describe the
possible lengths of the third side.
 a) 12 inches and 16 inches
 b) 4 feet and 10 feet
EXAMPLES
 EX 4: You are asked to fence in a triangular playground. Two
sides of the playground have lengths of 100 feet and 200 feet.
What is the maximum total length of fence you could
possibly need?
5.5 p. 298
6 – 11 all, 14 – 18 evens, 24, 25, 29 – 31
all, 34, 42 – 45 all
19 questions