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:

Problem 1: $\overline{PR}$

Step1: Identify segment parts

From the diagram, $PR$ is part of $PS$? Wait, no—wait, the diagram shows $P$, $R$, $S$ with $PR$? Wait, no, looking at the first problem: $P$ to $R$? Wait, the length from $P$ to $R$? Wait, the diagram has $P$---$R$---$S$, with $PS = 5.8$ mm and $RS = 3.7$ mm? Wait, no, maybe $PR$ is $PS - RS$? Wait, no, maybe $PR$ is the segment from $P$ to $R$, and $RS$ is from $R$ to $S$. Wait, the problem says "Find the measure of each segment" for $\overline{PR}$. Wait, maybe the diagram is $P$---$R$---$S$, with $PS = 5.8$ mm and $RS = 3.7$ mm? Wait, no, maybe $PR$ is $PS - RS$? Wait, no, maybe $PR$ is $5.8 - 3.7$? Wait, no, maybe I misread. Wait, the first problem: $\overline{PR}$. Let's check the diagram: $P$ has a segment to $R$, then $R$ to $S$, with $PS = 5.8$ mm and $RS = 3.7$ mm? Wait, no, maybe $PR$ is $PS - RS$? Wait, $PS = PR + RS$, so $PR = PS - RS$. So $PS = 5.8$ mm, $RS = 3.7$ mm. So $PR = 5.8 - 3.7 = 2.1$ mm? Wait, no, maybe the other way. Wait, maybe $P$ to $R$ is $5.8 - 3.7$? Wait, let's confirm. If $P$---$R$---$S$, then $PS = PR + RS$. So $PR = PS - RS = 5.8 - 3.7 = 2.1$ mm.

Step1: Determine formula

$PR = PS - RS$ (segment addition postulate: $PS = PR + RS$ ⇒ $PR = PS - RS$)

Step2: Substitute values

$PS = 5.8$ mm, $RS = 3.7$ mm
$PR = 5.8 - 3.7 = 2.1$ mm

Step1: Segment addition

$EF = EG + GF$ (since $E$---$G$---$F$)

Step2: Substitute values

$EG = 2.5$ in, $GF = 2.8$ in
$EF = 2.5 + 2.8 = 5.3$ in

Step1: Segment addition

$JL = JK + KL$ (since $J$---$K$---$L$)

Step2: Substitute values

$JK = 0.75$ cm, $KL = 0.35$ cm
$JL = 0.75 + 0.35 = 1.1$ cm

Answer:

$2.1$ mm

Problem 2: $\overline{EF}$