Question

use the segment addition postulate to find the missing lengths. 9. ab = 2, bc = 8, ac =? 10. ab = 7, bc = 7, ac =? 11. ac = 19, ab = 17, bc =? 12. ab = 3, ac = 11, bc =? 13. bc = 7, ab = 14, ac =?

Explanation:

Step1: Recall segment - addition postulate

If B is between A and C, then \(AC = AB+BC\), \(BC=AC - AB\), \(AB = AC - BC\)

Step2: Solve problem 9

Given \(AB = 2\), \(BC = 8\). Using \(AC=AB + BC\), we have \(AC=2 + 8=10\)

Step3: Solve problem 10

Given \(AB = 7\), \(BC = 7\). Using \(AC=AB + BC\), we have \(AC=7 + 7 = 14\)

Step4: Solve problem 11

Given \(AC = 19\), \(AB = 17\). Using \(BC=AC - AB\), we have \(BC=19 - 17=2\)

Step5: Solve problem 12

Given \(AB = 3\), \(AC = 11\). Using \(BC=AC - AB\), we have \(BC=11 - 3 = 8\)

Step6: Solve problem 13

Given \(BC = 7\), \(AB = 14\). Using \(AC=AB + BC\), we have \(AC=14 + 7=21\)

Answer:

1. \(AC = 10\)
2. \(AC = 14\)
3. \(BC = 2\)
4. \(BC = 8\)
5. \(AC = 21\)