4.3 Triangle Inequalities
______________________________ – An angle that forms a linear pair with one of the interior
angles of a triangle.
______________________________ – The interior angle that forms a linear pair with a given
exterior angle of a triangle.
______________________________ (of the exterior angle of a triangle) – The two interior angles
that do not share a vertex with the exterior angle.
exterior a ngle
adj acent interior angle
remote interior angle s
Triangle Inequality Conjecture
The sum of any two sides of a triangle is _____________ than the length of the third side.
Side-Angle Inequality Conjecture
In a triangle, if one side is longer than another side, then the angle opposite the longer side is
_______________ than the angle opposite the shorter side.
Triangle Exterior Angle Conjecture
The measure of an exterior angle of a triangle is ______________ to the sum of the measures of the
remote interior angles.
Geometry Lesson 4.3: Triangle Inequalities
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Example 1: Determine whether it is possible to draw a triangle with sides of the given measures.
a)
8 cm, 10 cm, 12 cm
b)
2 in, 5 in, 7 in
c)
6 m, 9 m, 14 m
d)
9 cm, 12 cm, 15 cm
Example 2: The measures of two sides of a triangle are given. Find the range of possible measures
for the third side.
a. 11 inches and 13 inches
b. 12 inches and 15 inches
c. 9 inches and 13 inches
Geometry Lesson 4.3: Triangle Inequalities
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Example 3: Arrange the unknown measures in order from least to greatest.
n
m
j
k
70
43
65
o
71
l
p
32
27
r
q
Example 4: Find the missing angle measures.
s + t = ______
s
u = _______
150
t
u
133
64
v = w = ________
v
w
132
Geometry Lesson 4.3: Triangle Inequalities
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Example 5: Find the value of x in each.
a. x = _______
b. x = _______
86
93
122
x
c. x = _______
123
x
d. x = _______
88
96
x
129
Geometry Lesson 4.3: Triangle Inequalities
x
125
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Example 6: Find a, b, and c in each.
a. a = _______ b = _______ c = _______
b. a = _______ b = _______ c = _______
a
a
121
b
128
b
c
c
c. a = _______ b = _______ c = _______
a
126
b
c
Homework: pp. 216 – 217 => 1 - 16
Geometry Lesson 4.3: Triangle Inequalities
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