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5.6 Inequalities in One Triangle
N#____ ____/____/____
A#____ ___/___/___
PWS 5.6 #’s 1-23
Exterior Angle Inequality - An exterior
angle of a triangle must be greater than
each of its remote interior angles.
1
m4  m1
m4  m2
4
2
Explain why
E1
E2
3
2
3
2
1
1
Exterior Angle Inequality
Angle 1 is an exterior
angle and angle 2 is a
remote interior
Exterior Angle Inequality
Angle 1 is an exterior angle and
angle 3 is a remote interior.
Vertical Angles
Angle 3 is congruent to angle 2
Transitive Property
Angle 1 is > angle 3 and angle 3 = angle
2. Therefore, angle 1 is > angle 2
Angle Side Relationships in Triangles
If one side of a triangle is longer than
another side of the triangle, then the
angle opposite the longer side will be
greater than the angle opposite the
A
shorter side.
AB  AC 
mC  mB
8
B
5
C
Angle Side Relationships in Triangles
If one angle of a triangle is greater than
another angle of the triangle, then the
side opposite the greater angle will be
longer than the side opposite the lesser
A
angle.
mC  mB 
AB  AC
B
35
50
C
E3 List the angles of triangle ABC in
order from least to greatest.
A
12
B, C , A
B
9
14
C
E4 List the sides of triangle ABC in order
from least to greatest.
A
70
B
AC , AB, BC
50
60
C
E5 Determine which sides is shortest in
the diagram.
A
48
85
D
DB or DA ?
95
47
45
B
40
C
The two shorter sides of a triangle must
be longer than the third side.
B
FACT
A
C
Is it possible to form a triangle with the
given side lengths? Explain why.
E 6 6, 8, 14
E 7 15, 16, 30
E8 2, 8, 11
6  8  14?
NO!
15  16  30? YES !!
2  8  11?
NO!
Given 2 sides of a triangle you can find
the range of the third side by adding
and subtracting the two sides that you
have and plugging them into the
following inequality.
Subract  x  Add
52  x  5 2
3 x  7
5
2
x
Find the range for the measure of the third side
of a triangle given the measures of two sides.
E 9 3ft, 7ft
4 ft  x  10 ft
E10 60km, 93km
33km  x  153km
E11 7.2m, 19.4m
12.2m  x  26.6m
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