Question

based on the given lengths, determine whether the segments can form a triangle.
drag each set of side lengths to the correct location on the table.

can form a triangle | cant form a triangle

3, 4, 9
7, 5, 12
7, 8, 9
2, 4, 7
4, 6, 8
3, 7, 11
3, 6, 7
6, 8, 11

Explanation:

State the Triangle Inequality Theorem

For any three side lengths \(a\), \(b\), and \(c\) (where \(a \le b \le c\)), they can form a triangle if and only if:

$$ a + b > c $$

Evaluate each set of side lengths

• For \(3, 4, 9\): \(3 + 4 = 7

gtr 9\) (Can't Form)

• For \(7, 5, 12\): \(5 + 7 = 12

gtr 12\) (Can't Form)

• For \(7, 8, 9\): \(7 + 8 = 15 > 9\) (Can Form)
• For \(2, 4, 7\): \(2 + 4 = 6

gtr 7\) (Can't Form)

• For \(4, 6, 8\): \(4 + 6 = 10 > 8\) (Can Form)
• For \(3, 7, 11\): \(3 + 7 = 10

gtr 11\) (Can't Form)

• For \(3, 6, 7\): \(3 + 6 = 9 > 7\) (Can Form)
• For \(6, 8, 11\): \(6 + 8 = 14 > 11\) (Can Form)

Group the sets into the table categories

• Can Form a Triangle:
• \(7, 8, 9\)
• \(4, 6, 8\)
• \(3, 6, 7\)
• \(6, 8, 11\)

• Can't Form a Triangle:
• \(3, 4, 9\)
• \(7, 5, 12\)
• \(2, 4, 7\)
• \(3, 7, 11\)

Answer:

Can Form a Triangle	Can't Form a Triangle
\(4, 6, 8\)	\(7, 5, 12\)
\(3, 6, 7\)	\(2, 4, 7\)
\(6, 8, 11\)	\(3, 7, 11\)