Question

name: __________ pd. ________ date. __________
\\(\overline{ck}\\) is 174 centimeters long.

1. find cg.
2. find gk.

use the number line.
is each statement true or false?

1. (ce + eh=ch)
2. (dj + jg = dg)

Explanation:

Step1: Set up an equation for the length of $\overline{CK}$

Since $CK = CG+GK$ and $CG = 8w + 5$, $GK=5w$, and $CK = 174$, we have the equation $(8w + 5)+5w=174$.

Step2: Combine like - terms

Combining the $w$ terms on the left - hand side gives $13w + 5=174$.

Step3: Solve for $w$

Subtract 5 from both sides: $13w=174 - 5=169$. Then divide both sides by 13: $w=\frac{169}{13}=13$.

Step4: Find $CG$

Substitute $w = 13$ into the expression for $CG$: $CG=8w + 5=8\times13+5=104 + 5=109$ centimeters.

Step5: Find $GK$

Substitute $w = 13$ into the expression for $GK$: $GK=5w=5\times13 = 65$ centimeters.

Step6: Check segment addition postulate for 3

On the number - line, for points $C$, $E$, and $H$, by the segment addition postulate, if $E$ is between $C$ and $H$, then $CE+EH = CH$. So the statement $CE + EH=CH$ is True.

Step7: Check segment addition postulate for 4

On the number - line, for points $D$, $J$, and $G$, since $J$ is not between $D$ and $G$, $DJ+JG
eq DG$. So the statement $DJ + JG=DG$ is False.

Answer:

1. $CG = 109$ centimeters
2. $GK = 65$ centimeters
3. True
4. False