Triangle Inequality Worksheet
Triangle Inequality
Properties of Triangles • Worksheet
Name:
Date:
The Triangle Inequality Theorem: For any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
1. Sides: 12, 15, 20
12
15
20
Show Work:
Triangle
No
2. Sides: 5, 8, 15
5
8
15
Show Work:
Triangle
No
3. Sides: 45, 30, 70
45
30
70
Show Work:
Triangle
No
4. Sides: 10, 10, 20
10
10
20
Show Work:
Triangle
No
5. Sides: 25, 25, 25
25
25
25
Show Work:
Triangle
No
6. Sides: 90, 10, 95
90
10
95
Show Work:
Triangle
No
7. Sides: 3, 4, 10
3
4
10
Show Work:
Triangle
No
8. Sides: 62, 28, 40
62
28
40
Show Work:
Triangle
No
9. Sides: 80, 50, 40
80
50
40
Show Work:
Triangle
No
10. Sides: 100, 10, 10
100
10
10
Show Work:
Triangle
No
Part II: Problem Solving
11. Construct a triangle using three pieces of wire: 35 cm, 42 cm, and 75 cm. Is it possible? Show reasoning.
12. Two sides of a triangle are 15 inches and 25 inches. What is the range of whole number lengths for the 3rd side?
13. A plot of land has boundary lengths 80m and 60m. Could the third boundary be 150m? Explain using math.
Part III: Error Analysis
Student Claim (A):
"Sides: 10, 20, 30. Sum: 10 + 20 = 30. Since they match the third side, it's a triangle."
Explain the mistake and what would happen if you tried to build this triangle.
Student Claim (B):
"Sides: 40, 50, 100. 100 + 40 > 50, so it's a triangle."
Explain the mistake and show the correct way to test these lengths.
Triangle Inequality Answer Key
Answer Key: Triangle Inequality
Grading Guide • Visual Analysis (1-4)
1. 12, 15, 20 Triangle
Correct Work:
12 + 15 = 27
27 > 20 (True)
2. 5, 8, 15 No
Correct Work:
5 + 8 = 13
13 is not > 15 (False)
3. 45, 30, 70 Triangle
Correct Work:
30 + 45 = 75
75 > 70 (True)
4. 10, 10, 20 No
Correct Work:
10 + 10 = 20
20 is not > 20 (False)
Triangle Inequality Answer Key • Page 2
5. 25, 25, 25 Triangle
25+25=50 > 25 ✔
6. 90, 10, 95 Triangle
90+10=100 > 95 ✔
7. 3, 4, 10 No
3+4=7 < 10 ✘
8. 62, 28, 40 Triangle
28+40=68 > 62 ✔
9. 80, 50, 40 Triangle
50+40=90 > 80 ✔
10. 100, 10, 10 No
10+10=20 < 100 ✘
Triangle Inequality Answer Key • Page 3
Part II: Problem Solving Answers
11. Possible? 35, 42, 75
YES. 35 + 42 = 77. Since the sum of the two shorter sides (77) is greater than the third side (75), a triangle can be formed.
12. Third side range: 15, 25
11 to 39 inches. Range formula: (Difference < x < Sum). 25 - 15 = 10; 25 + 15 = 40. Possible whole numbers: 11, 12 ... 39.
13. Boundary 150m? (80m, 60m)
NO. 80 + 60 = 140. Since 140 is less than 150, the segments cannot meet to enclose the plot.
Part III: Error Analysis Answers
Correct Reasoning (A):
Claim is Incorrect. The sum must be strictly greater than the third side. If 10 + 20 = 30, the lines will lie perfectly flat on top of the 30cm side, making a single line segment instead of a triangle.
Correct Reasoning (B):
Claim is Incorrect. The student checked the wrong sides. You must always check if the two shortest sides added together are greater than the longest side. 40 + 50 = 90. 90 is not greater than 100.
