Question

examples 1 and 2
find the measure of each segment.

1. $overline{pr}$
2. $overline{ef}$
3. $overline{jl}$
4. $overline{hj}$
5. $overline{ac}$
6. $overline{sv}$
7. $overline{nq}$
8. $overline{ac}$
9. $overline{gh}$

Explanation:

Step1: Identify segment - length relationships

For each segment, we use the property that if a point lies on a line - segment, the length of the whole segment is the sum of the lengths of its sub - segments.

Step2: Calculate length of $\overline{PR}$

Given $PS = 5.8$ mm and $RS = 3.7$ mm, then $PR=PS - RS$. So, $PR = 5.8-3.7=2.1$ mm.

Step3: Calculate length of $\overline{EF}$

Given $EG = 2.5$ in and $GF = 2.8$ in, then $EF=EG + GF$. So, $EF = 2.5+2.8 = 5.3$ in.

Step4: Calculate length of $\overline{JL}$

Given $JK = 0.75$ cm and $KL = 0.35$ cm, then $JL=JK + KL$. So, $JL = 0.75 + 0.35=1.1$ cm.

Step5: Calculate length of $\overline{HJ}$

Given $HK = 12.2$ ft and $JK = 3.1$ ft, then $HJ=HK - JK$. So, $HJ = 12.2-3.1 = 9.1$ ft.

Step6: Calculate length of $\overline{AC}$

Given $AB = 0.4$ m and $BC = 1.6$ m, then $AC=AB + BC$. So, $AC = 0.4+1.6 = 2$ m.

Step7: Calculate length of $\overline{SV}$

Given $ST = 4.1$ in and $VT = 2.6$ in, then $SV=ST - VT$. So, $SV = 4.1-2.6 = 1.5$ in.

Step8: Calculate length of $\overline{NQ}$

Given $NP = 1\frac{1}{4}$ in and $QP = 1$ in, then $NQ=NP + QP$. Since $1\frac{1}{4}=1.25$, $NQ = 1 + 1.25=2.25$ in.

Step9: Calculate length of $\overline{AC}$

Given $AB = 4.9$ cm and $BC = 5.2$ cm, then $AC=AB + BC$. So, $AC = 4.9+5.2 = 10.1$ cm.

Step10: Calculate length of $\overline{GH}$

Given $FH = 15$ mm and $FG = 9.7$ mm, then $GH=FH - FG$. So, $GH = 15 - 9.7 = 5.3$ mm.

Answer:

1. $\overline{PR}=2.1$ mm
2. $\overline{EF}=5.3$ in
3. $\overline{JL}=1.1$ cm
4. $\overline{HJ}=9.1$ ft
5. $\overline{AC}=2$ m
6. $\overline{SV}=1.5$ in
7. $\overline{NQ}=2.25$ in
8. $\overline{AC}=10.1$ cm
9. $\overline{GH}=5.3$ mm