Q10. Classify each pair of lines as i... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 3: Q10. (page 75)

Classify each pair of lines as intersecting, parallel, or skew.
a. $\overset{鈫�}{A B}$ and $\overset{鈫�}{E J}$
b. $\overset{鈫�}{A B}$ and $\overset{鈫�}{F K}$
c. $\overset{鈫�}{A B}$ and width="18" height="23" role="math">ID鈫�
d. $\overset{鈫�}{E F}$ and $\overset{鈫�}{I H}$
e. $\overset{鈫�}{E F}$ and $\overset{鈫�}{N M}$
f. $\overset{鈫�}{C N}$ and $\overset{鈫�}{F G}$

Short Answer

Expert verified

a. $\overset{鈫�}{A B}$ and $\overset{鈫�}{E J}$ are parallel lines

b. $\overset{鈫�}{A B}$ and $\overset{鈫�}{F K}$ are parallel lines

c. $\overset{鈫�}{A B}$ and $\overset{鈫�}{I D}$ are skew lines

d. $\overset{鈫�}{E F}$ and $\overset{鈫�}{I H}$ are intersecting lines

e. $\overset{鈫�}{E F}$ and $\overset{鈫�}{N M}$ are intersecting lines

f. $\overset{鈫�}{C N}$ and $\overset{鈫�}{F G}$ 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, $\overset{鈫�}{A B}$ and $\overset{鈫�}{E J}$ 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, $\overset{鈫�}{A B}$ and $\overset{鈫�}{F K}$ 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, $\overset{鈫�}{A B}$ and $\overset{鈫�}{I D}$ 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, $\overset{鈫�}{E F}$ and $\overset{鈫�}{I H}$ 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, $\overset{鈫�}{E F}$ and $\overset{鈫�}{N M}$ 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, $\overset{鈫�}{C N}$ and $\overset{鈫�}{F G}$ are skew lines

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Short Answer

Step by step solution

Part a. Step 1. Intersecting lines.

Part a. Step 2. Parallel Lines.

Part a. Step 3. Skew lines.

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

Part b. Step 1. Intersecting lines.

Part b. Step 2. Parallel Lines.

Part b. Step 3. Skew lines.

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

Part c. Step 1. Intersecting lines.

Part c. Step 2. Parallel Lines.

Part c. Step 3. Skew lines.

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

Part d. Step 1. Intersecting lines.

Part d. Step 2. Parallel Lines.

Part d. Step 3. Skew lines.

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

Part e. Step 1. Intersecting lines.

Part e. Step 2. Parallel Lines.

Part e. Step 3. Skew lines.

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

Part f. Step 1. Intersecting lines.

Part f. Step 2. Parallel Lines.

Part f. Step 3. Skew lines.

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

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91影视

Classify each pair of lines as intersecting, parallel, or skew.a.AB鈫� andEJ鈫�b.AB鈫� andFK鈫�c.AB鈫�and width="18" height="23" role="math">ID鈫�d.EF鈫� andIH鈫�e. EF鈫�and NM鈫�f. CN鈫� andFG鈫�

Short Answer

Step by step solution

Part a. Step 1. Intersecting lines.

Part a. Step 2. Parallel Lines.

Part a. Step 3. Skew lines.

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

Part b. Step 1. Intersecting lines.

Part b. Step 2. Parallel Lines.

Part b. Step 3. Skew lines.

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

Part c. Step 1. Intersecting lines.

Part c. Step 2. Parallel Lines.

Part c. Step 3. Skew lines.

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

Part d. Step 1. Intersecting lines.

Part d. Step 2. Parallel Lines.

Part d. Step 3. Skew lines.

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

Part e. Step 1. Intersecting lines.

Part e. Step 2. Parallel Lines.

Part e. Step 3. Skew lines.

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

Part f. Step 1. Intersecting lines.

Part f. Step 2. Parallel Lines.

Part f. Step 3. Skew lines.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Pure Maths

Calculus

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.