Question

g.co.c.10: triangle inequality theorem
1 which numbers could represent the lengths of the sides of a triangle?

1. 5,9,14
2. 7,7,15
3. 1,2,4
4. 3,6,8

2 which set of numbers represents the lengths of the sides of a triangle?

1. {5,18,13}
2. {6,17,22}
3. {16,24,7}
4. {26,8,15}

3 phil is cutting a triangular piece of tile. if the triangle is scalene, which set of numbers could represent the lengths of the sides?

1. {2,4,7}
2. {4,5,6}
3. {3,5,8}
4. {5,5,8}

4 which set can not represent the lengths of the sides of a triangle?

1. {4,5,6}
2. {5,5,11}
3. {7,7,12}
4. {8,8,8}

5 which set could not represent the lengths of the sides of a triangle?

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

6 in △abc, ab = 5 feet and bc = 3 feet. which inequality represents all possible values for the length of ac, in feet?

1. 2≤ac≤8
2. 2<ac<8
3. 3≤ac≤7
4. 3<ac<7

7 the lengths of two sides of a triangle are 7 and 11. which inequality represents all possible values for x, the length of the third side of the triangle?

1. 4≤x≤18
2. 4<x≤18
3. 4≤x<18
4. 4<x<18

8 if two sides of a triangle are 1 and 3, the third side may be

1. 5
2. 2
3. 3
4. 4

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Analyze question 1

1. For 5, 9, 14: \(5 + 9=14\), does not satisfy the theorem.
2. For 7, 7, 15: \(7+7 = 14<15\), does not satisfy the theorem.
3. For 1, 2, 4: \(1 + 2=3<4\), does not satisfy the theorem.
4. For 3, 6, 8: \(3 + 6>8\), \(3+8>6\), \(6 + 8>3\), satisfies the theorem. So the answer is 4.

Step3: Analyze question 2

1. For \(\{5,18,13\}\): \(5+13 = 18\), does not satisfy the theorem.
2. For \(\{6,17,22\}\): \(6 + 17>22\), \(6+22>17\), \(17 + 22>6\), satisfies the theorem.
3. For \(\{16,24,7\}\): \(7+16 = 23<24\), does not satisfy the theorem.
4. For \(\{26,8,15\}\): \(8 + 15=23<26\), does not satisfy the theorem. So the answer is 2.

Step4: Analyze question 3

1. For \(\{2,4,7\}\): \(2+4 = 6<7\), does not satisfy the theorem.
2. For \(\{4,5,6\}\): \(4 + 5>6\), \(4+6>5\), \(5 + 6>4\), and it is scalene.
3. For \(\{3,5,8\}\): \(3+5 = 8\), does not satisfy the theorem.
4. For \(\{5,5,8\}\): is isosceles, not scalene. So the answer is 2.

Step5: Analyze question 4

1. For \(\{4,5,6\}\): \(4 + 5>6\), \(4+6>5\), \(5 + 6>4\), satisfies the theorem.
2. For \(\{5,5,11\}\): \(5+5 = 10<11\), does not satisfy the theorem.
3. For \(\{7,7,12\}\): \(7+7>12\), \(7 + 12>7\), satisfies the theorem.
4. For \(\{8,8,8\}\): satisfies the theorem. So the answer is 2.

Step6: Analyze question 5

1. For \(\{3,4,5\}\): \(3 + 4>5\), \(3+5>4\), \(4 + 5>3\), satisfies the theorem.
2. For \(\{2,5,9\}\): \(2+5 = 7<9\), does not satisfy the theorem.
3. For \(\{5,10,12\}\): \(5+10>12\), \(5 + 12>10\), \(10+12>5\), satisfies the theorem.
4. For \(\{7,9,11\}\): \(7+9>11\), \(7 + 11>9\), \(9+11>7\), satisfies the theorem. So the answer is 2.

Step7: Analyze question 6

According to the triangle - inequality theorem, \(|AB - BC|

Step8: Analyze question 7

Let the two sides be \(a = 7\) and \(b = 11\). Then \(|b - a|

Step9: Analyze question 8

Let the two sides be \(a = 1\) and \(b = 3\). Then \(|b - a|

Answer:

1. 4
2. 2
3. 2
4. 2
5. 2
6. 2
7. 4
8. 3