Let’s go through each triangle one by one.
We use the
Triangle Inequality Theorem:
> The sum of any two sides must be greater than the third side.
So for sides a, b, c:
- a + b > c
- a + c > b
- b + c > a
If even one of these is false, the triangle is NOT possible.
---
1) Sides: 4 in, 5 in, 1 in
Check:
4 + 5 = 9 > 1
✔
4 + 1 = 5 → NOT greater than 5
✘ (must be strictly greater)
→ Not possible
2) Sides: 4 ft, 2 ft, 2 ft
Check:
4 + 2 = 6 > 2
✔
2 + 2 = 4 → NOT greater than 4
✘
→ Not possible
3) Sides: 6 yd, 5 yd, 9 yd
Check:
6 + 5 = 11 > 9
✔
6 + 9 = 15 > 5
✔
5 + 9 = 14 > 6
✔
→ Possible
4) Sides: 5 yd, 3 yd, 5 yd
Check:
5 + 3 = 8 > 5
✔
5 + 5 = 10 > 3
✔
3 + 5 = 8 > 5
✔
→ Possible
5) Sides: 4 in, 5 in, 8 in
Check:
4 + 5 = 9 > 8
✔
4 + 8 = 12 > 5
✔
5 + 8 = 13 > 4
✔
→ Possible
6) Sides: 3 ft, 5 ft, 7 ft
Check:
3 + 5 = 8 > 7
✔
3 + 7 = 10 > 5
✔
5 + 7 = 12 > 3
✔
→ Possible
7) Sides: 7 in, 7 in, 7 in (equilateral)
All sums: 7+7=14 > 7
✔
→ Possible
8) Sides: 10 yd, 4 yd, 5 yd
Check:
4 + 5 = 9 → NOT greater than 10
✘
→ Not possible
9) Sides: 4 in, 4 in, 8 in
Check:
4 + 4 = 8 → NOT greater than 8
✘
→ Not possible
10) Sides: 3 ft, 4 ft, 5 ft
Check:
3 + 4 = 7 > 5
✔
3 + 5 = 8 > 4
✔
4 + 5 = 9 > 3
✔
→ Possible
11) Sides: 5 in, 3 in, 4 in
Check:
5 + 3 = 8 > 4
✔
5 + 4 = 9 > 3
✔
3 + 4 = 7 > 5
✔
→ Possible
12) Sides: 6 yd, 6 yd, 6 yd
All same — obviously works.
6 + 6 = 12 > 6
✔
→ Possible
---
Final Answers:
1) Not possible
2) Not possible
3) Possible
4) Possible
5) Possible
6) Possible
7) Possible
8) Not possible
9) Not possible
10) Possible
11) Possible
12) Possible
Parent Tip: Review the logic above to help your child master the concept of triangle inequality theorem worksheet pdf.
