McDougal Littell Jurgensen Geometry: Student Edition Geometry

5th Edition

ISBN: 9780395977279

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

Publisher: Houghton Mifflin Company College Division

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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

Chapter 3.2, Problem 4MRE

(a)

To determine

To find: whether the statement is true or false.

(a)

Expert Solution

Answer to Problem 4MRE

The given statement is true.

Explanation of Solution

Given:

The statement is given as “Two planes are parallel only if they do not intersect”.

Calculation:

Consider the statement.

Two planes are parallel only if they do not intersect.

A plane can be considered to be consisted of several parallel lines lying in the plane.

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.2, Problem 4MRE

Figure 1

As it is clear from the figure that line A and Line B are parallel to each other, and they are not intersected.

Now, if the lines are not parallel, then they are going to intersect each other at some point.

That means, the two planes are parallel if they do not intersect each other.

Therefore, the given statement is true.

(b)

To determine

To find: the converse of the given statement.

(b)

Expert Solution

Answer to Problem 4MRE

If two planes do not intersect, then they are parallel.

Explanation of Solution

Given:

The converse of the statement is “Two planes are parallel only if they do not intersect”.

Calculation:

Consider the statement.

“Two planes are parallel only if they do not intersect”.

Recall that the converse of a statement “if p, then q” is given as “if q, then p”.

So, the converse of the given statement is “If two planes do not intersect, then they are parallel”.

(c)

To determine

To find: whether the converse of the statement is true or false.

(c)

Expert Solution

Answer to Problem 4MRE

The converse of the statement is true.

Explanation of Solution

Given:

The converse of the statement is “Two planes are parallel only if they do not intersect”.

Calculation:

Consider the statement.

“Two planes are parallel only if they do not intersect”.

The converse of the statement is,

“If two planes do not intersect, then they are parallel.”.

Consider that the two planes do not intersect. So, the angle between the two planes must be either 0 or 180 degrees.

If planes are considered to be consisted of serval parallel lines, the angle between the lines of two planes will also be either 0 or 180 degrees.

That means, the lines of one plane are parallel to the lines of the other planes. This implies that the planes are parallel.

Therefore, if two planes do not intersect, they must be parallel.

Hence, the converse of the statement is true.

Chapter 3.2, Problem 3MRE

Chapter 3.3, Problem 1CE

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 3.1 - Prob. 1CE Ch. 3.1 - Prob. 2CE Ch. 3.1 - Prob. 3CE Ch. 3.1 - Prob. 4CE Ch. 3.1 - Prob. 5CE Ch. 3.1 - Prob. 6CE Ch. 3.1 - Prob. 7CE Ch. 3.1 - Prob. 8CE Ch. 3.1 - Prob. 9CE Ch. 3.1 - Prob. 10CE

Ch. 3.1 - Prob. 11CE Ch. 3.1 - Prob. 12CE Ch. 3.1 - Prob. 13CE Ch. 3.1 - Prob. 14CE Ch. 3.1 - Prob. 15CE Ch. 3.1 - Prob. 16CE Ch. 3.1 - Prob. 17CE Ch. 3.1 - Prob. 18CE Ch. 3.1 - Prob. 19CE Ch. 3.1 - Prob. 1WE Ch. 3.1 - Prob. 2WE Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - Prob. 5WE Ch. 3.1 - Prob. 6WE Ch. 3.1 - Prob. 7WE Ch. 3.1 - Prob. 8WE Ch. 3.1 - Prob. 9WE Ch. 3.1 - Prob. 10WE Ch. 3.1 - Prob. 11WE Ch. 3.1 - Prob. 12WE Ch. 3.1 - Prob. 13WE Ch. 3.1 - Prob. 14WE Ch. 3.1 - Prob. 15WE Ch. 3.1 - Prob. 16WE Ch. 3.1 - Prob. 17WE Ch. 3.1 - Prob. 18WE Ch. 3.1 - Prob. 19WE Ch. 3.1 - Prob. 20WE Ch. 3.1 - Prob. 21WE Ch. 3.1 - Prob. 22WE Ch. 3.1 - Prob. 23WE Ch. 3.1 - Prob. 24WE Ch. 3.1 - Prob. 25WE Ch. 3.1 - Prob. 26WE Ch. 3.1 - Prob. 27WE Ch. 3.1 - Prob. 28WE Ch. 3.1 - Prob. 29WE Ch. 3.1 - Prob. 30WE Ch. 3.1 - Prob. 31WE Ch. 3.1 - Prob. 32WE Ch. 3.1 - Prob. 33WE Ch. 3.1 - Prob. 34WE Ch. 3.1 - Prob. 35WE Ch. 3.1 - Prob. 36WE Ch. 3.1 - Prob. 37WE Ch. 3.1 - Prob. 38WE Ch. 3.1 - Prob. 39WE Ch. 3.1 - 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Prob. 4CE Ch. 3.3 - Prob. 5CE Ch. 3.3 - Prob. 6CE Ch. 3.3 - Prob. 7CE Ch. 3.3 - Prob. 8CE Ch. 3.3 - Prob. 9CE Ch. 3.3 - Prob. 10CE Ch. 3.3 - Prob. 11CE Ch. 3.3 - Prob. 12CE Ch. 3.3 - Prob. 13CE Ch. 3.3 - Prob. 14CE Ch. 3.3 - Prob. 15CE Ch. 3.3 - Prob. 16CE Ch. 3.3 - Prob. 17CE Ch. 3.3 - Prob. 18CE Ch. 3.3 - Prob. 19CE Ch. 3.3 - Prob. 20CE Ch. 3.3 - Prob. 1WE Ch. 3.3 - Prob. 2WE Ch. 3.3 - Prob. 3WE Ch. 3.3 - Prob. 4WE Ch. 3.3 - Prob. 5WE Ch. 3.3 - Prob. 6WE Ch. 3.3 - Prob. 7WE Ch. 3.3 - Prob. 8WE Ch. 3.3 - Prob. 9WE Ch. 3.3 - Prob. 10WE Ch. 3.3 - Prob. 11WE Ch. 3.3 - Prob. 12WE Ch. 3.3 - Prob. 13WE Ch. 3.3 - Prob. 14WE Ch. 3.3 - Prob. 15WE Ch. 3.3 - Prob. 16WE Ch. 3.3 - Prob. 17WE Ch. 3.3 - Prob. 18WE Ch. 3.3 - Prob. 19WE Ch. 3.3 - Prob. 20WE Ch. 3.3 - Prob. 21WE Ch. 3.3 - Prob. 22WE Ch. 3.3 - Prob. 23WE Ch. 3.3 - Prob. 24WE Ch. 3.3 - Prob. 25WE Ch. 3.3 - Prob. 26WE Ch. 3.3 - Prob. 27WE Ch. 3.3 - Prob. 28WE Ch. 3.3 - Prob. 29WE Ch. 3.3 - Prob. 30WE Ch. 3.3 - Prob. 31WE Ch. 3.3 - Prob. 1ST1 Ch. 3.3 - Prob. 2ST1 Ch. 3.3 - Prob. 3ST1 Ch. 3.3 - Prob. 4ST1 Ch. 3.3 - Prob. 5ST1 Ch. 3.3 - Prob. 6ST1 Ch. 3.3 - Prob. 7ST1 Ch. 3.3 - Prob. 8ST1 Ch. 3.3 - Prob. 9ST1 Ch. 3.3 - Prob. 10ST1 Ch. 3.3 - Prob. 11ST1 Ch. 3.3 - Prob. 12ST1 Ch. 3.3 - Prob. 13ST1 Ch. 3.3 - Prob. 14ST1 Ch. 3.3 - Prob. 15ST1 Ch. 3.3 - Prob. 16ST1 Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.4 - Prob. 1CE Ch. 3.4 - Prob. 2CE Ch. 3.4 - Prob. 3CE Ch. 3.4 - Prob. 4CE Ch. 3.4 - Prob. 5CE Ch. 3.4 - Prob. 6CE Ch. 3.4 - Prob. 7CE Ch. 3.4 - Prob. 8CE Ch. 3.4 - Prob. 9CE Ch. 3.4 - Prob. 10CE Ch. 3.4 - Prob. 11CE Ch. 3.4 - Prob. 12CE Ch. 3.4 - Prob. 13CE Ch. 3.4 - Prob. 14CE Ch. 3.4 - Prob. 15CE Ch. 3.4 - Prob. 16CE Ch. 3.4 - Prob. 17CE Ch. 3.4 - Prob. 1WE Ch. 3.4 - Prob. 2WE Ch. 3.4 - Prob. 3WE Ch. 3.4 - Prob. 4WE Ch. 3.4 - Prob. 5WE Ch. 3.4 - Prob. 6WE Ch. 3.4 - Prob. 7WE Ch. 3.4 - Prob. 8WE Ch. 3.4 - Prob. 9WE Ch. 3.4 - 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Prob. 16WE Ch. 3.5 - Prob. 17WE Ch. 3.5 - Prob. 18WE Ch. 3.5 - Prob. 19WE Ch. 3.5 - Prob. 20WE Ch. 3.5 - Prob. 21WE Ch. 3.5 - Prob. 22WE Ch. 3.5 - Prob. 23WE Ch. 3.5 - Prob. 24WE Ch. 3.5 - Prob. 25WE Ch. 3.5 - Prob. 26WE Ch. 3.5 - Prob. 27WE Ch. 3.5 - Prob. 28WE Ch. 3.6 - Prob. 1CE Ch. 3.6 - Prob. 2CE Ch. 3.6 - Prob. 3CE Ch. 3.6 - Prob. 4CE Ch. 3.6 - Prob. 5CE Ch. 3.6 - Prob. 6CE Ch. 3.6 - Prob. 1WE Ch. 3.6 - Prob. 2WE Ch. 3.6 - Prob. 3WE Ch. 3.6 - Prob. 4WE Ch. 3.6 - Prob. 5WE Ch. 3.6 - Prob. 6WE Ch. 3.6 - Prob. 7WE Ch. 3.6 - Prob. 8WE Ch. 3.6 - Prob. 9WE Ch. 3.6 - Prob. 10WE Ch. 3.6 - Prob. 11WE Ch. 3.6 - Prob. 12WE Ch. 3.6 - Prob. 13WE Ch. 3.6 - Prob. 14WE Ch. 3.6 - Prob. 15WE Ch. 3.6 - Prob. 16WE Ch. 3.6 - Prob. 17WE Ch. 3.6 - Prob. 18WE Ch. 3.6 - Prob. 19WE Ch. 3.6 - Prob. 20WE Ch. 3.6 - Prob. 21WE Ch. 3.6 - Prob. 22WE Ch. 3.6 - Prob. 23WE Ch. 3.6 - Prob. 24WE Ch. 3.6 - Prob. 25WE Ch. 3.6 - Prob. 26WE Ch. 3.6 - Prob. 27WE Ch. 3.6 - Prob. 28WE Ch. 3.6 - Prob. 29WE Ch. 3.6 - Prob. 30WE Ch. 3.6 - Prob. 1ST2 Ch. 3.6 - Prob. 2ST2 Ch. 3.6 - Prob. 3ST2 Ch. 3.6 - Prob. 4ST2 Ch. 3.6 - Prob. 5ST2 Ch. 3.6 - Prob. 6ST2 Ch. 3.6 - Prob. 7ST2 Ch. 3.6 - Prob. 8ST2 Ch. 3.6 - Prob. 9ST2 Ch. 3.6 - Prob. 10ST2 Ch. 3.6 - Prob. 11ST2 Ch. 3.6 - Prob. 12ST2 Ch. 3.6 - Prob. 13ST2 Ch. 3.6 - Prob. 14ST2 Ch. 3.6 - Prob. 15ST2 Ch. 3 - Prob. 1CR Ch. 3 - Prob. 2CR Ch. 3 - Prob. 3CR Ch. 3 - Prob. 4CR Ch. 3 - Prob. 5CR Ch. 3 - Prob. 6CR Ch. 3 - Prob. 7CR Ch. 3 - Prob. 8CR Ch. 3 - Prob. 9CR Ch. 3 - Prob. 10CR Ch. 3 - Prob. 11CR Ch. 3 - Prob. 12CR Ch. 3 - Prob. 13CR Ch. 3 - Prob. 14CR Ch. 3 - Prob. 15CR Ch. 3 - Prob. 16CR Ch. 3 - Prob. 17CR Ch. 3 - Prob. 18CR Ch. 3 - Prob. 19CR Ch. 3 - Prob. 20CR Ch. 3 - Prob. 21CR Ch. 3 - Prob. 1CT Ch. 3 - Prob. 2CT Ch. 3 - Prob. 3CT Ch. 3 - Prob. 4CT Ch. 3 - Prob. 5CT Ch. 3 - Prob. 6CT Ch. 3 - Prob. 7CT Ch. 3 - Prob. 8CT Ch. 3 - Prob. 9CT Ch. 3 - Prob. 10CT Ch. 3 - Prob. 11CT Ch. 3 - Prob. 12CT Ch. 3 - Prob. 13CT Ch. 3 - Prob. 14CT Ch. 3 - Prob. 1AR Ch. 3 - Prob. 2AR Ch. 3 - 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