Question

1.2 segments homework
find the measurement of each segment. assume that the art is not drawn to scale.

1. \\( \overline { r t } \\)
2. \\( \overline { b c } \\)
3. \\( \overline { x z } \\)
4. \\( \overline { w x } \\)

Explanation:

1. For \(\overline{RT}\)

Step1: Use segment addition postulate

The segment addition postulate states that if \(R - S - T\), then \(RT=RS + ST\).

Step2: Substitute the values

Given \(RS = 2.0\mathrm{cm}\) and \(ST=2.5\mathrm{cm}\), then \(RT=2.0 + 2.5\).

$$RT=(2 + 2)+(0.0+0.5)=4.5\mathrm{cm}$$

2. For \(\overline{BC}\)

Step1: Use segment addition postulate

If \(A - B - C\), then \(AC=AB + BC\), so \(BC=AC - AB\).

Step2: Convert the mixed - number

\(AB = 2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}\) and \(AC = 6=\frac{24}{4}\).

Step3: Calculate \(BC\)

$$BC=\frac{24}{4}-\frac{11}{4}=\frac{24 - 11}{4}=\frac{13}{4}=3\frac{1}{4}\text{in}$$

3. For \(\overline{XZ}\)

Step1: Use segment addition postulate

If \(X - Y - Z\), then \(XZ=XY+YZ\).

Step2: Convert the mixed - number

\(XY = 3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{7}{2}=\frac{14}{4}\) and \(YZ=\frac{3}{4}\).

Step3: Calculate \(XZ\)

$$XZ=\frac{14}{4}+\frac{3}{4}=\frac{14 + 3}{4}=\frac{17}{4}=4\frac{1}{4}\text{in}$$

4. For \(\overline{WX}\)

Step1: Use the property of congruent segments

Since \(WX=XY\) and \(WY = WX+XY\), and \(WY = 6\mathrm{cm}\).

Step2: Solve for \(WX\)

Let \(WX=x\), then \(x + x=6\), \(2x=6\), \(x = 3\mathrm{cm}\).

Answer:

1. \(4.5\mathrm{cm}\)
2. \(3\frac{1}{4}\text{in}\)
3. \(4\frac{1}{4}\text{in}\)
4. \(3\mathrm{cm}\)