1. Lesson: 7 – 4 Triangle Inequality Theorem
Applied Geometry
Lesson: 7 – 4
Triangle Inequality Theorem
Objective:
Learn to identify and use the Triangle Inequality Theorem.

2. Using a ruler draw a triangle with the following measurements (cm).
5, 7, 4 11, 3, 7 3, 4, 5
1, 1.5, 3 16, 10, 5 7, 10, 12

3. Triangle Inequality Theorem
The sum of the measures of any two sides of a triangle is greater than the measure of the third side.

4. 5, 7, 4 11, 3, 7 16, 10, 5 5 + 7 > 4 Yes, it is a triangle.
Determine if the three numbers can be measures of the sides of a triangle.
5, 7, 4
11, 3, 7
16, 10, 5
5 + 7 > 4
Yes, it is a triangle.
7 + 4 > 5
5 + 4 > 7
> 7
No, it is not a triangle.
3 + 7 > 11
> 5
No, it is not a triangle.
> 16

5. So the greatest and least WHOLE NUMBER measures
What are the greatest and least possible whole number measures for the 3rd side? x
Write the 3 inequalities.
> x
10 + x > 7
7 + x > 10
x > 3
17 > x
x > -3
Can’t have a negative side.
x has to be less than 17, but greater than 3.
So the greatest and least WHOLE NUMBER measures
are 16 cm & 4 cm.

6. 10 inches & 6 inches. 8 + 3 > x 3 + x > 8 x > 5 11> x
What are the greatest and least possible whole-number measures for the third side of a triangle if the other two sides measure 8 inches and 3 inches?
8 + 3 > x
3 + x > 8
x > 5
11> x
10 inches & 6 inches.

7. 4 + 4 > x 4 + x > 4 x > 0 8 > x 0 < x < 8
The measure of the third side is bigger than 0, but less than 8
0 < x < 8

8. 9 + 13 > x 9 + x > 13 22 > x x > 4 4 < x < 22
If the measures of two sides of a triangle are 9 and 13, find the range of possible measures of the third side.
> x
9 + x > 13
22 > x
x > 4
4 < x < 22

9. Homework
Pg – 8 all, 10 – 30 E