 Students
will be able to use inequalities
involving angles and sides of triangles
 The
angles and sides of triangles have
special relationships involving
inequalities
 Properties
of Inequalities
 Addition Property
• If a > b and c ≥ d, then a + c > b + d
 Multiplication
Property
• If a > b and c > 0, then ac > bc
• If a > b and c < 0 then ac < bc
 Transitive
Property
• If a > b and b > c, then a > c
 Use
addition, subtraction, multiplication,
and division properties to solve
inequalities
 Same idea as solving equations
 If you divide by a negative number
remember to reverse to inequality
symbol
 7x
– 13 ≤ -20
 8y
+ 2 ≥ 14
 -3(4x
 3x
– 1) ≥ 15
– 5x + 2 < 12
 If
a = b + c and c > 0, then a > b
 Used to prove the corollary to the
Triangle Exterior Angle Theorem
 What is the Triangle Exterior Angle
Theorem?
 The
measure of an exterior angle is
greater than the measure of each remote
interior angles of a triangle
 Why
is m<2 > m<3?
 Why is m<5 > m<C?
 If
two sides of a triangle are not
congruent, the the larger angle lies
opposite the longer side

A town park is triangular. A landscape
architect wants to place a bench at the
corner with the largest angle. Which two
streets form the corner
with the larges angle?

Now suppose the architect wants to place
a drinking fountain at the corner with the
second largest angle. Which two streets
form the corner with the
second largest angle?
 If
two angles of a triangle are not
congruent, then the longer side lies
opposite the larger angle
 <S
= 24 and <O = 130. Which side of
ΔSOX is the shortest side? Explain.
 In
order to form or construct a triangle
the sum of the two shortest sides must be
greater than the largest side.
 Can
a triangle have sides with the given
lengths?
 3 ft, 7 ft, 8 ft?
2
m, 6m, 9m?
4
yd, 6yd, 9yd?
 Use
x to represent the third side
 You will need to write three inequalities.
One to represent each side of the
triangle it could be
 Then write an inequality that represents
the answers
A
triangle has sides lengths of 4in and
7in. What is the range of possible side
lengths for the third side?
 Pg. 328
#
6 – 29 all
 24 problems