use the diagram below for problems 1 - 3.
1. which of the following is a pair of skew lines?
a. ab and cd b. cd and bd c. hd and ge
d. gh and ab e. hd and cg
2. which lines are parallel to fh?
a. ef, gh, and bf b. cg, cd, and ab
c. ac, eg, and bd d. eg, cg, and cd
e. dh, cd, and ae
3. which lines are perpendicular to fh?
a. ef, gh, and bf b. cg, cd, and ab c. ac, eg, and bd
d. eg, cg, and cd e. dh, cd, and ae

Question

Accepted Answer

# Explanation:
## 1. Skew Lines
### Step1: Recall Skew Lines Definition
Skew lines are non - parallel and non - intersecting lines in 3 - D space.
- $AB$ and $CD$ are parallel (in the same plane of the top and bottom rectangles of the prism).
- $CD$ and $BD$ intersect at point $D$.
- $HD$ and $GE$: $HD$ is in the plane $CDHG$ and $GE$ is in the plane $ABFE$. They are non - parallel and non - intersecting.
- $GH$ and $AB$ are parallel (by the properties of the prism).
- $HD$ and $CG$ are parallel (in the plane $CDHG$).

## 2. Parallel Lines to $FH$
### Step1: Use Parallel Line Properties
In a prism, lines that have the same direction (vector) are parallel.
- $FH$ is a vertical line (assuming the standard orientation of the prism). $EG$, $CG$, and $CD$ are all vertical lines (by the structure of the rectangular prism).
- For option a: $EF$ is horizontal, $GH$ is horizontal (parallel to each other but not to $FH$).
- For option b: $CG$ is vertical, but $CD$ and $AB$ are horizontal.
- For option c: $AC$, $EG$, and $BD$: $AC$ and $BD$ are diagonal lines in their respective planes.
- For option e: $DH$ is vertical, but $CD$ and $AE$ are not vertical.

## 3. Perpendicular Lines to $FH$
### Step1: Use Perpendicular Line Properties
If a line is vertical ($FH$ is vertical in the assumed orientation),  horizontal lines in the planes that intersect the line of $FH$ are perpendicular to it.
- $EF$, $GH$, and $BF$: $EF$ and $GH$ are horizontal (in the top and bottom planes respectively), and $BF$ is also horizontal (in the side - face plane).
- For option b: $CG$ is vertical (parallel to $FH$ if $FH$ is vertical).
- For option c: $AC$, $EG$, and $BD$: $EG$ is vertical (parallel to $FH$ if $FH$ is vertical).
- For option d: $EG$ and $CG$ are vertical (parallel to $FH$ if $FH$ is vertical).
- For option e: $DH$ is vertical (parallel to $FH$ if $FH$ is vertical).

# Answer:
1. c. $HD$ and $GE$
2. d. $EG$, $CG$, and $CD$
3. a. $EF$, $GH$, and $BF$

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QUESTION IMAGE

Question

Explanation:

1. Skew Lines

Step1: Recall Skew Lines Definition

2. Parallel Lines to \(FH\)

Step1: Use Parallel Line Properties

3. Perpendicular Lines to \(FH\)

Step1: Use Perpendicular Line Properties

Answer: