The document discusses inequalities between sides and angles of triangles. It states that if the measures of the sides of a triangle are unequal, then the measures of the angles opposite those sides are unequal in the same order (Theorem 7-6). Similarly, if the measures of the angles of a triangle are unequal, then the measures of the sides opposite those angles are unequal in the same order (Theorem 7-7). It also discusses the triangle inequality theorem, which states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.

1. Inequalities Within a TriangleInequalities Within a Triangle
You will learn to identify the relationships between the _____
and _____ of a triangle.
sides
angles
Nothing New!

2. Inequalities Within a TriangleInequalities Within a Triangle
Theorem 7 – 6
If the measures of three sides of a triangle are unequal,
then the measures of the angles opposite those sides
are unequal ________________.
13
8
11
L
P
M
in the same order
LP < PM < ML

3. Inequalities Within a TriangleInequalities Within a Triangle
Theorem 7 – 7
If the measures of three angles of a triangle are unequal,
then the measures of the sides opposite those angles
are unequal ________________.in the same order
JK < KW < WJ
J
45°
W K
60°
75°

4. Inequalities Within a TriangleInequalities Within a Triangle
Theorem 7 – 8
In a right triangle, the hypotenuse is the side with the
________________.greatest measure
WY > XW
3
5
4 Y
W
X
WY > XY

5. Inequalities Within a TriangleInequalities Within a Triangle
A∠
The longest side is BC
So, the largest angle is
L∠The largest angle is
MNSo, the longest side is

6. Triangle Inequality TheoremTriangle Inequality Theorem
You will learn to identify and use the
Triangle Inequality Theorem.
Nothing New!

7. Triangle Inequality TheoremTriangle Inequality Theorem
Theorem 7 – 9
Triangle
Inequality
Theorem
The sum of the measures of any two sides of a triangle is
_______ than the measure of the third side.greater
a
b
c
a + b > c
a + c > b
b + c > a

8. Triangle Inequality TheoremTriangle Inequality Theorem
Can 16, 10, and 5 be the measures of the sides of a triangle?
No! 16 + 10 > 5
16 + 5 > 10
However, 10 + 5 > 16

9. The measures of two sides of a triangle
are given. Between what two numbers
must the third side fall.
9 and 15
15 – 9 = 6
15 + 9 = 24
6 < x < 24
9 15
x

10. The measures of two sides of a triangle
are given. Between what two numbers
must the third side fall.
9 and 15
15 – 9 = 6
15 + 9 = 24
6 < x < 24
9 15
x