Question

c is between a and e. for each problem, draw a picture representing the three points and information given. solve for indicated. 5. if ac = 24 in. and ce = 13 in., ae = __. 6. if ce = 7in. and ae = 23 in., ac = __. find qr in the following problems. r is between q and s. 7. if rs = 44.6 and sq = 68.4, find qr. 8. if rs = 33.5 and rq = 80, find sq.

Explanation:

Step1: Use segment - addition postulate

Since \(C\) is between \(A\) and \(E\), \(AE=AC + CE\).

Step2: Solve for \(AE\) in problem 5

Given \(AC = 24\) in and \(CE=13\) in, then \(AE=24 + 13=37\) in.

Step3: Use segment - addition postulate for problem 6

Since \(AE=AC + CE\), then \(AC=AE - CE\).

Step4: Solve for \(AC\) in problem 6

Given \(CE = 7\) in and \(AE = 23\) in, then \(AC=23 - 7 = 16\) in.

Step5: Use segment - addition postulate for problem 7

Since \(R\) is between \(Q\) and \(S\), \(SQ=QR+RS\), then \(QR=SQ - RS\).

Step6: Solve for \(QR\) in problem 7

Given \(RS = 44.6\) and \(SQ = 68.4\), then \(QR=68.4 - 44.6 = 23.8\).

Step7: Use segment - addition postulate for problem 8

Since \(SQ=RQ + RS\).

Step8: Solve for \(SQ\) in problem 8

Given \(RS = 33.5\) and \(RQ = 80\), then \(SQ=80 + 33.5=113.5\).

Answer:

1. \(37\) in
2. \(16\) in
3. \(23.8\)
4. \(113.5\)