Question

1. complete the activity below, answering all of the questions.
2. when you have finished the guided practice activity, upload a screenshot of your score screen to earn credit for this activity.

triangle inequality theorem
state if the three numbers can be the measures of the sides of a triangle.

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

two sides of a triangle have the following measures. find the range of possible measures for the third side.

1. 9, 12
2. 7, 7
3. 10, 8
4. 7, 11
5. 7, 12

Explanation:

Step1: Check triangle inequality for each set

For three side lengths \(a\), \(b\), \(c\) of a triangle, the following must hold: \(a + b>c\), \(a + c>b\), \(b + c>a\)

1) \(a = 8\), \(b = 8\), \(c = 12\)

• \(8+8 = 16>12\)
• \(8 + 12=20>8\)
• \(8+12 = 20>8\)

So, yes

2) \(a = 9\), \(b = 11\), \(c = 6\)

• \(9+11=20>6\)
• \(9 + 6=15>11\)
• \(11+6 = 17>9\)

So, yes

3) \(a = 8\), \(b = 3\), \(c = 11\)

• \(8+3=11\) (not greater than \(11\))

So, no

4) \(a = 6\), \(b = 14\), \(c = 7\)

• \(6+7=13<14\)

So, no

5) \(a = 6\), \(b = 11\), \(c = 16\)

• \(6+11=17>16\)
• \(6 + 16=22>11\)
• \(11+16 = 27>6\)

So, yes

6) \(a = 9\), \(b = 12\)

Let the third side be \(x\). By triangle - inequality: \(12 - 9

7) \(a = 7\), \(b = 7\)

Let the third side be \(x\). By triangle - inequality: \(7 - 7

8) \(a = 10\), \(b = 8\)

Let the third side be \(x\). By triangle - inequality: \(10 - 8

9) \(a = 7\), \(b = 11\)

Let the third side be \(x\). By triangle - inequality: \(11 - 7

10) \(a = 7\), \(b = 12\)

Let the third side be \(x\). By triangle - inequality: \(12 - 7

Answer:

1. Yes
2. Yes
3. No
4. No
5. Yes
6. \(3
7. \(0
8. \(2
9. \(4
10. \(5