Download PP Section 6.5

Geometry Section 6.5
Inequalities in One Triangle
What you will learn:
1. List sides and angles of triangles in order by
size.
2. Use the Triangle Inequality Theorem to find
possible side lengths of triangles.
The Base Angles Theorem states “If two sides
of a triangle are congruent, then the angles
opposite them are congruent.” The following
theorem covers the case where two sides of a
triangle are not congruent.
Theorem 6.9: Triangle Longer Side Theorem
If one side of a triangle is longer than another
side, then the angle opposite the longer side
is larger than the angle opposite the shorter
side.
Theorem 6.10: Triangle Larger Angle Theorem
If one angle of a triangle is larger than
another angle, then the side opposite the
larger angle is longer than the side opposite
the smaller angle.
mC  mA  mB
mD  180  107  38  35
DF  DE  EF
Theorem 6.11 Triangle Inequality Theorem
The sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.
AB  BC  AC
AB  AC  BC
BC  AC  AB
Examples: Which of the following are possible lengths for the
sides of a triangle?
a) 14, 8, 25
b) 16, 7, 23
c) 18, 8, 24
YES
Examples: The lengths of two sides of a triangle are
given. Write a compound inequality (two inequalities in
one) that expresses the possible values of x, the length
of the third side.
a) 7, 13
6
b) 8, 8
23
_____ < x < _____
0
16
_____ < x < _____
HW: pp 341-343 /
12-24 EVEN, 29, 30, 33, 37, 38, 44, 45