Question

geometry ch. 1 review name leguall show all work! use the figure to the right to answer questions 1 - 3. use appropriate symbols! 1) give two other names for $overrightarrow{rq}$: __, 2) name two opposite rays with endpoint p: , 3) name two segments on $overleftrightarrow{ar}$: , 4) sketch a picture of three collinear points and then sketch a picture of three non - collinear points 5) $wz = 40$, $xz = 28$, $overline{xy}congoverline{yz}$. find the length of $overline{wx},overline{xy},overline{yz}$. 6) draw a picture of segment $overline{jk}$ where midpoint and include tick marks. now label your picture with $jh$, $hk = 7x + 3$. solve for x and find indicated lengths. , $xy=$ , $yz=$ x = , $jh=$ __ 8) a) what are two

Explanation:

Step1: Identify alternative ray names

A ray is named by its endpoint and another point on the ray. For $\overrightarrow{RQ}$, two other names are $\overrightarrow{R}$ (since it's the same ray starting from $R$ going towards $Q$) and $\overrightarrow{RB}$ (assuming $B$ is a point further along the ray's path).

Step2: Find opposite rays with endpoint $P$

Opposite rays are two rays that have the same endpoint and form a straight - line. $\overrightarrow{PA}$ and $\overrightarrow{PC}$ are opposite rays with endpoint $P$.

Step3: Name segments on $\overleftrightarrow{AR}$

Segments are parts of a line with two endpoints. On $\overleftrightarrow{AR}$, two segments are $\overline{AP}$ and $\overline{PR}$.

Step4: Sketch collinear and non - collinear points

For collinear points, draw three points on a straight line. For non - collinear points, draw three points that do not lie on the same straight line.

Step5: Calculate segment lengths

Since $\overline{XY}\cong\overline{YZ}$ and $XZ = 28$, then $XY=YZ=\frac{XZ}{2}=\frac{28}{2} = 14$. And $WX=WZ - XZ=40 - 28 = 12$.

Step6: Solve for $x$ in segment problem

Since $H$ is the mid - point of $\overline{JK}$, $JH = HK$. Let $JH=HK$. If $JH = 5x- 1$ and $HK = 7x+3$, then $5x-1=7x + 3$.
Subtract $5x$ from both sides: $-1=2x + 3$.
Subtract 3 from both sides: $-4 = 2x$.
Divide both sides by 2: $x=-2$. Then $JH=5x-1=5(-2)-1=-10 - 1=-11$ (lengths should be non - negative in a geometric sense, there may be an error in the setup of the problem values).

Answer:

1. $\overrightarrow{R}$, $\overrightarrow{RB}$
2. $\overrightarrow{PA}$, $\overrightarrow{PC}$
3. $\overline{AP}$, $\overline{PR}$
4. (Sketch three points on a straight line for collinear and three points not on a straight line for non - collinear)
5. $WX = 12$, $XY = 14$, $YZ = 14$
6. $x=-2$, $JH=-11$ (check problem setup for non - negative length)