HomeRoots Pitch Deck | Investor Insights | April 2024
7-3 Triangle Inequalities
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
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