Question

simplify
mn = 30 + 8
no = 8(5) - 2
simplify
mn = 38
no = 40 - 2
segment addition postulate
mn + no = mo
substitute
38 + 38 = mo
simplify
76 = mo
your turn

1. b is the midpoint of \overline{ac}. find ab, bc, and ac.
2. rs = 4x - 6 and st = 3x + 4. find rt.

Explanation:

Step1: Use the mid - point property

Since \(B\) is the mid - point of \(\overline{AC}\), then \(AB = BC\). So, \(3x=5x - 6\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(0 = 5x-3x - 6\), which simplifies to \(0 = 2x - 6\). Then add \(6\) to both sides: \(6 = 2x\). Divide both sides by \(2\): \(x = 3\).

Step3: Calculate \(AB\)

Substitute \(x = 3\) into the expression for \(AB\). \(AB=3x\), so \(AB = 3\times3=9\).

Step4: Calculate \(BC\)

Substitute \(x = 3\) into the expression for \(BC\). \(BC = 5x-6\), so \(BC=5\times3 - 6=15 - 6 = 9\).

Step5: Calculate \(AC\)

Since \(AC=AB + BC\) (Segment Addition Postulate), \(AC=9 + 9=18\).

Answer:

\(AB = 9\), \(BC = 9\), \(AC = 18\)