Geometry Lab
The Triangle
Inequality Theorem
In this lab you will investigate whether it is possible to form a triangle with sides of
different lengths.
Activity
Step 1 Use a ruler to cut several straws into sections that measure 1, 2, 3, 4, 5,
6, 7, and 8 inches long.
2 in.
3 in.
4 in.
Step 2 Arrange the 2, 3, and 4 inch long pieces so that they form a triangle.
3 in.
2 in.
4 in.
Step 3 Copy the table below. Try to build a triangle with the different
combinations of given side lengths. If a triangle can be made, enter yes
in the table. If a triangle cannot be made, enter no.
Length of
First Piece (in.)
Length of
Second Piece (in.)
Length of
Third Piece (in.)
Triangle?
2
3
4
Yes
1
2
3
4
5
8
5
6
7
1
4
5
3
5
6
2
3
5
4
5
7
2
4
6
1
2
4
578 | Extend 10-3 | Geometry Lab: The Triangle Inequality Theorem
Analyze the Results
1. What combinations of side lengths created a triangle? What combinations
did not create a triangle?
2. Using your table, find the sums of the lengths of the first piece and the
second piece. What do you notice about the sums of the sides that created
triangles and the sums that did not create triangles?
3. MAKE A CONJECTURE Do you think it is possible to create a triangle with sides
that measure 2 inches, 2 inches, and 4 inches long? Explain.
4. WRITING IN MATH Based on the Activity, write a rule that can be used to
determine if any three lengths can be used to make a triangle.
In the Activity above, you found that a special relationship exists among the
lengths of the segments of a triangle. This is called the Triangle Inequality
Theorem.
KeyConcept Triangle Inequality Theorem
Words
The sum of the lengths of any two sides
of a triangle must be greater than the
length of the third side.
Symbols
AB + BC > AC
Model
B
AC + BC > AB
AB + AC > BC
A
C
Exercises
Determine if it is possible to form a triangle with the given side lengths. If
not, explain why not.
5. 3 in., 4 in., 8 in.
6. 2 mm, 2 mm, 8 mm
8. 7 yd, 8 yd, 9 yd
9. 3 cm, 6 cm, 9 cm
11. 18 m, 20 m, 40 m
12. 5 ft, 5 ft, 10 ft
7. 12 ft, 18 ft., 16 ft
10. 15 in., 12 in., 2 in.
13. 7 mm, 5 mm, 14 mm
Determine the least possible measure of the third side of a triangle with the
given side lengths if the missing measure is a whole number.
14. 12 m, 15 m
15. 8 in., 10 in.
16. 6 cm, 6 cm
17. 22 ft, 18 ft
18. 30 mm, 28 mm
19. 4 yd, 5 yd
20. 20 cm, 14 cm
21. 9 m, 12 m
22. 13 ft, 11 ft
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