Download Side-Angle Inequality Conjecture

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.
Lesson 4.3 Triangle Inequalities 1
Example 1: The measures of two sides of a triangle are given. Find the range of
possible measures for the third side.
a. 11 inches and 8 inches
b. 14 inches and 11 inches
c. 5 inches and 8 inches
Example 2: Find the missing angle measures.
s + t = ______
s
u = _______
150
t
u
133
64
v = w = ________
v
w
132
Lesson 4.3 Triangle Inequalities 2
Example 3: Arrange the unknown measures in order from least to greatest.
55°
b
c
30°
f
d
68°
a
60°
e
l
32°
m
n
61°
Example 4: Find the value of x in each.
a.
b.
87°
60°
113°
x
116°
x
c.
d.
88°
96°
x
129°
x
Lesson 4.3 Triangle Inequalities 3
125°
Example 5: Find a, b, and c in each.
a. a = ______ b = ______ c = ______
a
121°
b
c
b. a= ______ b = ______ c = ______
a
126°
b
c
c. a= ______ b = ______ c = _______
a
128°
b
c
Homework: Page 216 – 217 # 1 - 16
Lesson 4.3 Triangle Inequalities 4