Countdown Challenge: Triangle Inequality Theorem Worksheet for 7th ... - Free Printable

Final Answer:
A: Yes — triangle (2 + 2 > 4? No → Wait! 2 + 2 = 4, not greater → Not a triangle)
B: Yes — triangle (3 + 4 > 5 → 7 > 5 ✔️; 3 + 5 > 4 → 8 > 4 ✔️; 4 + 5 > 3 → 9 > 3 ✔️)
C: No — not a triangle (1 + 2 = 3, not greater → fails)
D: Yes — triangle (5 + 6 > 7 → 11 > 7 ✔️; etc.)
E: No — not a triangle (2 + 3 = 5, not greater than 5)

But wait—the table in the problem gives specific measurements. Let’s read them carefully from the table:

Row A: Lengths 2 cm, 2 cm, 4 cm
→ 2 + 2 = 4 → not greater → ✘ Not a triangle

Row B: 3 cm, 4 cm, 5 cm
→ 3+4=7 >5, 3+5=8>4, 4+5=9>3 → ✔ Triangle

Row C: 1 cm, 2 cm, 3 cm
→ 1+2=3 → not >3 → ✘ Not a triangle

Row D: 5 cm, 6 cm, 7 cm
→ 5+6=11>7, 5+7=12>6, 6+7=13>5 → ✔ Triangle

Row E: 2 cm, 3 cm, 5 cm
→ 2+3=5 → not >5 → ✘ Not a triangle

Now for “Type of triangle” (by sides):
- A: 2,2,4 → would be isosceles *if* it were a triangle, but it’s not → N/A
- B: 3,4,5 → all different → scalene
- C: not a triangle
- D: 5,6,7 → all different → scalene
- E: not a triangle

For angles (using longest side squared vs sum of squares of other two):
- B: 3²+4² = 9+16=25 = 5² → right triangle
- D: 5²+6² = 25+36=61 < 7²=49? Wait—7²=49, 61 > 49 → actually 5²+6²=61 > 49 → acute triangle
(Check: longest side = 7, so compare 5²+6² = 61 vs 7² = 49 → 61 > 49 → acute)

So final filled table:

| Shape | Lengths (cm) | Sum of two shorter > longest? | Triangle? | Type (sides) | Type (angles) |
|-------|--------------|-------------------------------|-----------|--------------|----------------|
| A | 2, 2, 4 | 2+2 = 4 → no | No | — | — |
| B | 3, 4, 5 | 3+4 > 5 → yes | Yes | Scalene | Right |
| C | 1, 2, 3 | 1+2 = 3 → no | No | — | — |
| D | 5, 6, 7 | 5+6 > 7 → yes | Yes | Scalene | Acute |
| E | 2, 3, 5 | 2+3 = 5 → no | No | — | — |

But the question only asks: “To be a triangle or not to be a triangle?” and then fill the table.

Since the instruction says: *“Provide only the final correct answer.”*, and the main decision is whether each shape is a triangle:

Final Answer:
A: No
B: Yes
C: No
D: Yes
E: No