Question

name the angles from largest to smallest.
4.
5.
6.
lesson 4.7
name the sides from longest to shortest.
7.
8.
9.
can the side lengths form a triangle? explain.

1. 7, 8, 16
2. 5, 6, 10
3. 4.3, 5, 9
4. 4, 7, 11
5. 8, 11.9, 20
6. 18, 20, 37.5

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that for three side lengths \(a\), \(b\), and \(c\) to form a triangle, the sum of any two sides must be greater than the third side. Mathematically, this means \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check for 7, 8, 16

Let \(a = 7\), \(b = 8\), \(c = 16\).
First, check \(a + b\): \(7+8 = 15\).
Now, compare \(15\) with \(c = 16\). Since \(15<16\), the sum of the two smaller sides is not greater than the largest side.

Step3: Conclusion for 7, 8, 16

Since \(7 + 8
ot>16\), the side lengths 7, 8, and 16 cannot form a triangle.

Step4: Check for 5, 6, 10

Let \(a = 5\), \(b = 6\), \(c = 10\).
Check \(a + b\): \(5 + 6=11\), and \(11>10\).
Check \(a + c\): \(5+10 = 15\), and \(15>6\).
Check \(b + c\): \(6 + 10=16\), and \(16>5\).
Since all three inequalities hold, 5, 6, 10 can form a triangle.

Step5: Check for 4.3, 5, 9

Let \(a = 4.3\), \(b = 5\), \(c = 9\).
Check \(a + b\): \(4.3+5 = 9.3\), and \(9.3>9\).
Check \(a + c\): \(4.3+9 = 13.3\), and \(13.3>5\).
Check \(b + c\): \(5 + 9=14\), and \(14>4.3\).
Since all three inequalities hold, 4.3, 5, 9 can form a triangle.

Step6: Check for 4, 7, 11

Let \(a = 4\), \(b = 7\), \(c = 11\).
Check \(a + b\): \(4+7 = 11\). But the triangle inequality requires the sum to be greater than the third side, not equal. So \(4 + 7
ot>11\) (it is equal). Thus, 4, 7, 11 cannot form a triangle.

Step7: Check for 8, 11.9, 20

Let \(a = 8\), \(b = 11.9\), \(c = 20\).
Check \(a + b\): \(8+11.9 = 19.9\).
Compare \(19.9\) with \(c = 20\). Since \(19.9<20\), the sum of the two smaller sides is not greater than the largest side. So 8, 11.9, 20 cannot form a triangle.

Step8: Check for 18, 20, 37.5

Let \(a = 18\), \(b = 20\), \(c = 37.5\).
Check \(a + b\): \(18+20 = 38\).
Compare \(38\) with \(c = 37.5\). Since \(38>37.5\).
Check \(a + c\): \(18+37.5 = 55.5\), and \(55.5>20\).
Check \(b + c\): \(20+37.5 = 57.5\), and \(57.5>18\).
Since all three inequalities hold, 18, 20, 37.5 can form a triangle.

Answer:

s:

• For 7, 8, 16: No, because \(7 + 8=15<16\) (violates triangle inequality).
• For 5, 6, 10: Yes, because \(5 + 6>10\), \(5 + 10>6\), and \(6 + 10>5\).
• For 4.3, 5, 9: Yes, because \(4.3+5>9\), \(4.3 + 9>5\), and \(5 + 9>4.3\).
• For 4, 7, 11: No, because \(4 + 7 = 11\) (not greater than 11, violates triangle inequality).
• For 8, 11.9, 20: No, because \(8+11.9 = 19.9<20\) (violates triangle inequality).
• For 18, 20, 37.5: Yes, because \(18+20>37.5\), \(18 + 37.5>20\), and \(20+37.5>18\).