1. Objective- To use the Third Side Property to find the third side of a triangle given the other two.
5 ft.
7 ft. X
What could the value of x be?

2. Could the value of x be 100? 5 ft. 7 ft. X
X= 100 ft.
No, that would be ridiculous! The other two sides would never meet.

3. What is the maximum value x could be?
5 ft.
7 ft. X

4. What is the maximum value x could be?
5 ft.
7 ft. X

5. What is the maximum value x could be?
5 ft.
7 ft. X

6. What is the maximum value x could be?
5 ft.
7 ft. X

7. What is the maximum value x could be?
5 ft.
7 ft. X

8. What is the maximum value x could be?
5 ft.
7 ft. X
The value of x is now 12,
but is this a triangle?

9. No this is not a triangle, it is a straight line
No this is not a triangle, it is a straight line. The triangle has collapsed.
5 ft.
7 ft. X
If x = 12 the sides will make a line.
If x > 12 the sides will not touch.
Therefore, x < 12.
or X <

10. Triangle Inequality a b X
x < a + b or
a + b > x

11. Triangle Inequality The sum of any two sides must
always be larger than a third side
Which could be the sides of a triangle? 1)
Yes 2) No 3) No 4) No

12. Is there a limit to how small x could be?
5 ft.
7 ft. X
Obviously, x could not be a negative number or 0. In order to be a distance, it must be a positive real number.

13. Could x = 1?
5 ft.
7 ft. X
7 ft.
5 ft.
X=1
No, The third side would be too small.

14. What is the smallest value for x?
7 ft.
5 ft. X
Could the value of x be 2?

15. Once again, this would be impossible as it would create a straight line.
7 ft.
5 ft.
X=2
x simply must be greater than 2 in order to create a triangle.

16. So, x has both a maximum value and a minimum value
So, x has both a maximum value and a minimum value. We call this the Third Side Property.
5 ft.
7 ft. X
< x <
Or...

17. < < Third Side Property
The third side of a triangle must be between the sum and the difference of the other two sides.
Difference
of the other
two sides
Sum of
the other
two sides
Third
Side
<
<

18. What are the possible values of x?12 15 x
< x <
3 < x < 27

19. What are the possible values of x?9 13 x
< x <
4 < x < 22

20. Related Problem Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Farthest Case
= 16 miles A B C
6 miles
10 miles

21. Related Problem Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Less than 16 Miles A B C
6 miles
10 miles

22. Related Problem Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Less than 16 Miles A B
6 miles
10 miles C

23. Related Problem Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Less than 16 Miles A B
6 miles
10 miles C

24. Related Problem Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Less than 16 Miles A B
6 miles
10 miles C

25. Related Problem Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Less than 16 Miles A B
6 miles
10 miles C

26. Related Problem Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Less than 16 Miles A B
6 miles
10 miles C

27. Related Problem Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Less than 16 Miles A B
6 miles
10 miles C

28. Related Problem 4 x 16 Alice lives 6 miles from Betty. Carla
lives 10 miles from Betty. How far
could Alice and Carla live apart?
Shortest Case = 4 Miles A B
4 Miles
6 miles C
10 miles x