Question

triangles - classify, interior & exterior angles #2
state if the three numbers can be the measures of the sides of a triangle.

1. 11, 11, 14
2. 12, 8, 9
3. 7, 11, 3
4. 16, 11, 7
5. 9, 3, 11
6. 9, 11, 7

Explanation:

Step1: Triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), check if \(a + b>c\)

1) For \(a = 11\), \(b = 11\), \(c = 14\)

\(11+11 = 22>14\)

2) For \(a = 8\), \(b = 9\), \(c = 12\)

\(8 + 9=17>12\)

3) For \(a = 3\), \(b = 7\), \(c = 11\)

\(3+7 = 10<11\)

4) For \(a = 7\), \(b = 11\), \(c = 16\)

\(7+11=18>16\)

5) For \(a = 3\), \(b = 9\), \(c = 11\)

\(3 + 9=12>11\)

6) For \(a = 7\), \(b = 9\), \(c = 11\)

\(7+9 = 16>11\)

Answer:

1. Yes
2. Yes
3. No
4. Yes
5. Yes
6. Yes