Question

Classify each pair of lines as intersecting, parallel, or skew.

a.$\overleftrightarrow{AB}$ and$\overleftrightarrow{EJ}$

b.$\overleftrightarrow{AB}$ and$\overleftrightarrow{FK}$

c.$\overleftrightarrow{AB}$and width="18" height="23" role="math">ID↔

d.$\overleftrightarrow{EF}$ and$\overleftrightarrow{IH}$

e. $\overleftrightarrow{EF}$and $\overleftrightarrow{NM}$

f. $\overleftrightarrow{CN}$ and$\overleftrightarrow{FG}$

Short answer

a. $\overleftrightarrow{AB}$and$\overleftrightarrow{EJ}$ are parallel lines

b. $\overleftrightarrow{AB}$and$\overleftrightarrow{FK}$ are parallel lines

c. $\overleftrightarrow{AB}$and$\overleftrightarrow{ID}$ are skew lines

d. $\overleftrightarrow{EF}$and$\overleftrightarrow{IH}$ are intersecting lines

e. $\overleftrightarrow{EF}$and$\overleftrightarrow{NM}$ are intersecting lines

f. $\overleftrightarrow{CN}$and$\overleftrightarrow{FG}$ are skew lines

Step-by-step solution

Part a. Step 1. Intersecting lines.

These are two lines that have at least one common point

Part a. Step 2. Parallel Lines.

These are two coplanar lines that have no point in common.

Part a. Step 3. Skew lines.

These are two non-coplanar lines that have no point in common.

Part a. Step 4. Classify given line as one of these lines.

From the given diagram, it is clear that the lines are parallel.

Hence, $\overleftrightarrow{AB}$and$\overleftrightarrow{EJ}$ are parallel lines

Part b. Step 1. Intersecting lines.

These are two lines that have at least one common point

Part b. Step 2. Parallel Lines.

These are two coplanar lines that have no point in common.

Part b. Step 3. Skew lines.

These are two non-coplanar lines that have no point in common.

Part b. Step 4. Classify given line as one of these lines.

From the given diagram, it is clear that the lines are parallel.

Thus, $\overleftrightarrow{AB}$and$\overleftrightarrow{FK}$ are parallel lines

Part c. Step 1. Intersecting lines.

These are two lines that have at least one common point

Part c. Step 2. Parallel Lines.

These are two coplanar lines that have no point in common.

Part c. Step 3. Skew lines.

These are two non-coplanar lines that have no point in common.

Part c. Step 4. Classify given line as one of these lines.

From the given diagram, it is clear that the lines are skew.

Therefore, $\overleftrightarrow{AB}$and$\overleftrightarrow{ID}$ are skew lines

Part d. Step 1. Intersecting lines.

These are two lines that have at least one common point

Part d. Step 2. Parallel Lines.

These are two coplanar lines that have no point in common.

Part d. Step 3. Skew lines.

These are two non-coplanar lines that have no point in common.

Part d. Step 4 - Classify given line as one of these lines

From the given diagram, it is clear that the lines are intersecting.

Hence, $\overleftrightarrow{EF}$and$\overleftrightarrow{IH}$ are intersecting lines

Part e. Step 1. Intersecting lines.

These are two lines that have at least one common point

Part e. Step 2. Parallel Lines.

These are two coplanar lines that have no point in common.

Part e. Step 3. Skew lines.

These are two non-coplanar lines that have no point in common.

Part e. Step 4. Classify given line as one of these lines.

From the given diagram, it is clear that the lines are intersecting.

Hence, $\overleftrightarrow{EF}$and$\overleftrightarrow{NM}$ are intersecting lines

Part f. Step 1. Intersecting lines.

These are two lines that have at least one common point

Part f. Step 2. Parallel Lines.

These are two coplanar lines that have no point in common.

Part f. Step 3. Skew lines.

These are two non-coplanar lines that have no point in common.

Part f. Step 4. Classify given line as one of these lines.

From the given diagram, it is clear that the lines are skew.

Hence, $\overleftrightarrow{CN}$and$\overleftrightarrow{FG}$ are skew lines