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 1.5, Problem 18WE

(a)

To determine

To check: The postulate that guarantees the existence of the plane ABC, ABD, ACD, BCD .

(a)

Expert Solution

Answer to Problem 18WE

It is the postulate 7.

Explanation of Solution

Given information:

Consider the statements below and associated figure

Points A , B , C and D are four non coplanar points

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 1.5, Problem 18WE , additional homework tip 1

Formula used:

Through any 3 non collinear points there is exactly one plane

Calculation:

From Postulate 7, through any 3 non collinear points there is exactly one plane. From the figure, points A , B , C and D are non collinear points, therefore from above argument there will be exactly one plane through points A,B,C and A,B,D and A,C,D and B,C,D

Hence, the answer is postulate 7.

Conclusion:

It is the postulate 7.

(b)

To determine

To describe:The ruler postulate that guarantees the existence of point P between A and D .

(b)

Expert Solution

Explanation of Solution

Given information:

Consider the statements below and associated figure

Points A, B, C and D are four non coplanar points

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 1.5, Problem 18WE , additional homework tip 2

Formula used:

Through any 3 non collinear points there is exactly one plane

Calculation:

By Ruler Postulate, the distance between any two points equals the absolute value of the difference of coordinates. If P is between A and D , with the respective coordinates y, x , and z and assuming x < y < z

By the ruler postulate,

AP=|y−x|PD=|z−y|AD=|z−x|

But y-x is positive because x < y. By similar argument, z - y and z - x are positive.

Therefore,

AP+PD=y−x+z−y =z−xAP+PD=AD

Therefore, the assumption of P is between A and D is correct.

Hence, the answer is P between A and D is proved by ruler postulate.

Conclusion:

The answer is P between A and D is proved by ruler postulate.

(c)

To determine

To write:The postulate that guarantees the existence of BCP.

(c)

Expert Solution

Answer to Problem 18WE

The answer is postulate 7.

Explanation of Solution

Given information:

Consider the statements below and associated figure

Points A, B, C and D are four non coplanar points.

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 1.5, Problem 18WE , additional homework tip 3

Formula used:

Through any 3 non collinear points there is exactly one plane

Calculation:

From Postulate 7, through any 3 non collinear points there is exactly one plane. From the figure, points B, C and P are non collinear points therefore from above argument there will be exactly one plane through points B, C, P

Hence, the answer is postulate 7.

Conclusion:

The answer is postulate 7.

(d)

To determine

To show:how there are infinite number of planes through BC¯

(d)

Expert Solution

Answer to Problem 18WE

The infinite number of point on AD¯ to form 3 non-collinear points with B and C and postulate 7 guarantees the existence of a unique plane through each set of the three points.

Explanation of Solution

Given information:

Consider the statements below and associated figure

Points A, B, C and D are four non coplanar points

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 1.5, Problem 18WE , additional homework tip 4

Formula used:

Through any 3 non collinear points there is exactly one plane

Calculation:

From the definition, a line segment consists of infinite number of points. This implies, there are an infinite number of points on AD¯ . Therefore, there are an infinite number of non collinear points to match up with B and C.

From Postulate 7, through any 3 non collinear points there is exactly one plane which implies each set of the three points forms a unique plane.

Hence, the answer to is infinite number of point on AD¯ to form 3 non-collinear points with B and C and postulate 7 guarantees the existence of a unique plane through each set of the three points.

Conclusion:

The infinite number of point on AD¯ to form 3 non-collinear points with B and C and postulate 7 guarantees the existence of a unique plane through each set of the three points.

Chapter 1.5, Problem 17WE

Chapter 1.5, Problem 19WE

Chapter 1 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 1.1 - Prob. 1CE Ch. 1.1 - Prob. 2CE Ch. 1.1 - Prob. 3CE Ch. 1.1 - Prob. 4CE Ch. 1.1 - Prob. 5CE Ch. 1.1 - Prob. 6CE Ch. 1.1 - Prob. 7CE Ch. 1.1 - Prob. 8CE Ch. 1.1 - Prob. 1WE Ch. 1.1 - Prob. 2WE

Ch. 1.1 - Prob. 3WE Ch. 1.1 - Prob. 4WE Ch. 1.1 - Prob. 5WE Ch. 1.1 - Prob. 6WE Ch. 1.1 - Prob. 7WE Ch. 1.1 - Prob. 8WE Ch. 1.1 - Prob. 9WE Ch. 1.1 - Prob. 10WE Ch. 1.2 - Prob. 1CE Ch. 1.2 - Prob. 2CE Ch. 1.2 - Prob. 3CE Ch. 1.2 - Prob. 4CE Ch. 1.2 - Prob. 5CE Ch. 1.2 - Prob. 6CE Ch. 1.2 - Prob. 7CE Ch. 1.2 - Prob. 8CE Ch. 1.2 - Prob. 9CE Ch. 1.2 - Prob. 10CE Ch. 1.2 - Prob. 11CE Ch. 1.2 - Prob. 12CE Ch. 1.2 - Prob. 13CE Ch. 1.2 - Prob. 14CE Ch. 1.2 - Prob. 15CE Ch. 1.2 - Prob. 16CE Ch. 1.2 - Prob. 17CE Ch. 1.2 - Prob. 18CE Ch. 1.2 - Prob. 19CE Ch. 1.2 - Prob. 20CE Ch. 1.2 - Prob. 1WE Ch. 1.2 - Prob. 2WE Ch. 1.2 - Prob. 3WE Ch. 1.2 - Prob. 4WE Ch. 1.2 - Prob. 5WE Ch. 1.2 - Prob. 6WE Ch. 1.2 - Prob. 7WE Ch. 1.2 - Prob. 8WE Ch. 1.2 - Prob. 9WE Ch. 1.2 - Prob. 10WE Ch. 1.2 - Prob. 11WE Ch. 1.2 - Prob. 12WE Ch. 1.2 - Prob. 13WE Ch. 1.2 - Prob. 14WE Ch. 1.2 - Prob. 15WE Ch. 1.2 - Prob. 16WE Ch. 1.2 - Prob. 17WE Ch. 1.2 - Prob. 18WE Ch. 1.2 - Prob. 19WE Ch. 1.2 - Prob. 20WE Ch. 1.2 - Prob. 21WE Ch. 1.2 - Prob. 22WE Ch. 1.2 - Prob. 23WE Ch. 1.2 - Prob. 24WE Ch. 1.2 - Prob. 25WE Ch. 1.2 - Prob. 26WE Ch. 1.2 - Prob. 27WE Ch. 1.2 - Prob. 28WE Ch. 1.2 - Prob. 29WE Ch. 1.2 - Prob. 30WE Ch. 1.2 - Prob. 31WE Ch. 1.2 - Prob. 32WE Ch. 1.2 - Prob. 33WE Ch. 1.2 - Prob. 34WE Ch. 1.2 - Prob. 35WE Ch. 1.2 - Prob. 36WE Ch. 1.2 - Prob. 1ST1 Ch. 1.2 - Prob. 2ST1 Ch. 1.2 - Prob. 3ST1 Ch. 1.2 - Prob. 4ST1 Ch. 1.2 - Prob. 5ST1 Ch. 1.2 - Prob. 6ST1 Ch. 1.2 - Prob. 7ST1 Ch. 1.2 - Prob. 1AR Ch. 1.2 - Prob. 2AR Ch. 1.2 - Prob. 3AR Ch. 1.2 - Prob. 4AR Ch. 1.2 - Prob. 5AR Ch. 1.2 - Prob. 6AR Ch. 1.2 - Prob. 7AR Ch. 1.2 - Prob. 8AR Ch. 1.2 - Prob. 9AR Ch. 1.2 - Prob. 10AR Ch. 1.2 - Prob. 11AR Ch. 1.2 - Prob. 12AR Ch. 1.2 - Prob. 13AR Ch. 1.2 - Prob. 14AR Ch. 1.2 - Prob. 15AR Ch. 1.2 - Prob. 16AR Ch. 1.2 - Prob. 17AR Ch. 1.2 - Prob. 18AR Ch. 1.2 - Prob. 19AR Ch. 1.2 - Prob. 20AR Ch. 1.2 - Prob. 21AR Ch. 1.2 - Prob. 22AR Ch. 1.2 - Prob. 23AR Ch. 1.2 - Prob. 24AR Ch. 1.2 - Prob. 25AR Ch. 1.2 - Prob. 26AR Ch. 1.2 - Prob. 27AR Ch. 1.2 - Prob. 28AR Ch. 1.2 - Prob. 29AR Ch. 1.2 - Prob. 30AR Ch. 1.2 - Prob. 31AR Ch. 1.2 - Prob. 32AR Ch. 1.2 - Prob. 33AR Ch. 1.2 - Prob. 34AR Ch. 1.2 - Prob. 35AR Ch. 1.2 - Prob. 36AR Ch. 1.2 - Prob. 37AR Ch. 1.2 - Prob. 38AR Ch. 1.2 - Prob. 39AR Ch. 1.2 - Prob. 40AR Ch. 1.2 - Prob. 41AR Ch. 1.2 - Prob. 42AR Ch. 1.2 - Prob. 43AR Ch. 1.2 - Prob. 44AR Ch. 1.2 - Prob. 45AR Ch. 1.2 - Prob. 46AR Ch. 1.3 - Prob. 1CE Ch. 1.3 - Prob. 2CE Ch. 1.3 - Prob. 3CE Ch. 1.3 - Prob. 4CE Ch. 1.3 - Prob. 5CE Ch. 1.3 - Prob. 6CE Ch. 1.3 - Prob. 7CE Ch. 1.3 - Prob. 8CE Ch. 1.3 - Prob. 9CE Ch. 1.3 - Prob. 10CE Ch. 1.3 - Prob. 11CE Ch. 1.3 - Prob. 12CE Ch. 1.3 - Prob. 13CE Ch. 1.3 - Prob. 14CE Ch. 1.3 - Prob. 15CE Ch. 1.3 - Prob. 16CE Ch. 1.3 - Prob. 17CE Ch. 1.3 - Prob. 18CE Ch. 1.3 - Prob. 19CE Ch. 1.3 - Prob. 20CE Ch. 1.3 - Prob. 21CE Ch. 1.3 - Prob. 22CE Ch. 1.3 - Prob. 23CE Ch. 1.3 - Prob. 24CE Ch. 1.3 - Prob. 25CE Ch. 1.3 - Prob. 26CE Ch. 1.3 - Prob. 1WE Ch. 1.3 - Prob. 2WE Ch. 1.3 - Prob. 3WE Ch. 1.3 - Prob. 4WE Ch. 1.3 - Prob. 5WE Ch. 1.3 - Prob. 6WE Ch. 1.3 - Prob. 7WE Ch. 1.3 - Prob. 8WE Ch. 1.3 - Prob. 9WE Ch. 1.3 - Prob. 10WE Ch. 1.3 - Prob. 11WE Ch. 1.3 - Prob. 12WE Ch. 1.3 - Prob. 13WE Ch. 1.3 - Prob. 14WE Ch. 1.3 - Prob. 15WE Ch. 1.3 - Prob. 16WE Ch. 1.3 - Prob. 17WE Ch. 1.3 - Prob. 18WE Ch. 1.3 - Prob. 19WE Ch. 1.3 - Prob. 20WE Ch. 1.3 - Prob. 21WE Ch. 1.3 - Prob. 22WE Ch. 1.3 - Prob. 23WE Ch. 1.3 - Prob. 24WE Ch. 1.3 - Prob. 25WE Ch. 1.3 - Prob. 26WE Ch. 1.3 - Prob. 27WE Ch. 1.3 - Prob. 28WE Ch. 1.3 - Prob. 29WE Ch. 1.3 - Prob. 30WE Ch. 1.3 - Prob. 31WE Ch. 1.3 - Prob. 32WE Ch. 1.3 - Prob. 33WE Ch. 1.3 - Prob. 34WE Ch. 1.3 - Prob. 35WE Ch. 1.3 - Prob. 36WE Ch. 1.3 - Prob. 37WE Ch. 1.3 - Prob. 38WE Ch. 1.3 - Prob. 39WE Ch. 1.3 - Prob. 40WE Ch. 1.3 - Prob. 41WE Ch. 1.3 - Prob. 42WE Ch. 1.3 - Prob. 43WE Ch. 1.3 - Prob. 44WE Ch. 1.3 - Prob. 45WE Ch. 1.3 - Prob. 46WE Ch. 1.3 - Prob. 47WE Ch. 1.3 - Prob. 48WE Ch. 1.4 - Prob. 1CE Ch. 1.4 - Prob. 2CE Ch. 1.4 - Prob. 3CE Ch. 1.4 - Prob. 4CE Ch. 1.4 - Prob. 5CE Ch. 1.4 - Prob. 6CE Ch. 1.4 - Prob. 7CE Ch. 1.4 - Prob. 8CE Ch. 1.4 - Prob. 9CE Ch. 1.4 - Prob. 10CE Ch. 1.4 - Prob. 11CE Ch. 1.4 - Prob. 12CE Ch. 1.4 - Prob. 13CE Ch. 1.4 - Prob. 14CE Ch. 1.4 - Prob. 15CE Ch. 1.4 - Prob. 16CE Ch. 1.4 - Prob. 17CE Ch. 1.4 - Prob. 18CE Ch. 1.4 - Prob. 19CE Ch. 1.4 - Prob. 20CE Ch. 1.4 - Prob. 21CE Ch. 1.4 - Prob. 22CE Ch. 1.4 - Prob. 23CE Ch. 1.4 - Prob. 24CE Ch. 1.4 - Prob. 25CE Ch. 1.4 - Prob. 26CE Ch. 1.4 - Prob. 27CE Ch. 1.4 - Prob. 28CE Ch. 1.4 - Prob. 29CE Ch. 1.4 - Prob. 30CE Ch. 1.4 - Prob. 31CE Ch. 1.4 - Prob. 32CE Ch. 1.4 - Prob. 33CE Ch. 1.4 - Prob. 34CE Ch. 1.4 - Prob. 35CE Ch. 1.4 - Prob. 36CE Ch. 1.4 - Prob. 37CE Ch. 1.4 - Prob. 38CE Ch. 1.4 - Prob. 1WE Ch. 1.4 - Prob. 2WE Ch. 1.4 - Prob. 3WE Ch. 1.4 - Prob. 4WE Ch. 1.4 - Prob. 5WE Ch. 1.4 - Prob. 6WE Ch. 1.4 - Prob. 7WE Ch. 1.4 - Prob. 8WE Ch. 1.4 - Prob. 9WE Ch. 1.4 - Prob. 10WE Ch. 1.4 - Prob. 11WE Ch. 1.4 - Prob. 12WE Ch. 1.4 - Prob. 13WE Ch. 1.4 - Prob. 14WE Ch. 1.4 - Prob. 15WE Ch. 1.4 - Prob. 16WE Ch. 1.4 - Prob. 17WE Ch. 1.4 - Prob. 18WE Ch. 1.4 - Prob. 19WE Ch. 1.4 - Prob. 20WE Ch. 1.4 - Prob. 21WE Ch. 1.4 - Prob. 22WE Ch. 1.4 - Prob. 23WE Ch. 1.4 - Prob. 24WE Ch. 1.4 - Prob. 25WE Ch. 1.4 - Prob. 26WE Ch. 1.4 - Prob. 27WE Ch. 1.4 - Prob. 28WE Ch. 1.4 - Prob. 29WE Ch. 1.4 - Prob. 30WE Ch. 1.4 - Prob. 31WE Ch. 1.4 - Prob. 32WE Ch. 1.4 - Prob. 33WE Ch. 1.4 - Prob. 34WE Ch. 1.4 - Prob. 35WE Ch. 1.4 - Prob. 36WE Ch. 1.5 - Prob. 1CE Ch. 1.5 - Prob. 2CE Ch. 1.5 - Prob. 3CE Ch. 1.5 - Prob. 4CE Ch. 1.5 - Prob. 5CE Ch. 1.5 - Prob. 6CE Ch. 1.5 - Prob. 7CE Ch. 1.5 - Prob. 8CE Ch. 1.5 - Prob. 9CE Ch. 1.5 - Prob. 10CE Ch. 1.5 - Prob. 11CE Ch. 1.5 - Prob. 12CE Ch. 1.5 - Prob. 13CE Ch. 1.5 - Prob. 14CE Ch. 1.5 - Prob. 15CE Ch. 1.5 - Prob. 16CE Ch. 1.5 - Prob. 1WE Ch. 1.5 - Prob. 2WE Ch. 1.5 - Prob. 3WE Ch. 1.5 - Prob. 4WE Ch. 1.5 - Prob. 5WE Ch. 1.5 - Prob. 6WE Ch. 1.5 - Prob. 7WE Ch. 1.5 - Prob. 8WE Ch. 1.5 - Prob. 9WE Ch. 1.5 - Prob. 10WE Ch. 1.5 - Prob. 11WE Ch. 1.5 - Prob. 12WE Ch. 1.5 - Prob. 13WE Ch. 1.5 - Prob. 14WE Ch. 1.5 - Prob. 15WE Ch. 1.5 - Prob. 16WE Ch. 1.5 - Prob. 17WE Ch. 1.5 - Prob. 18WE Ch. 1.5 - Prob. 19WE Ch. 1.5 - Prob. 20WE Ch. 1.5 - Prob. 1E Ch. 1.5 - Prob. 2E Ch. 1.5 - Prob. 3E Ch. 1.5 - Prob. 4E Ch. 1.5 - Prob. 5E Ch. 1.5 - Prob. 6E Ch. 1.5 - Prob. 1ST2 Ch. 1.5 - Prob. 2ST2 Ch. 1.5 - Prob. 3ST2 Ch. 1.5 - Prob. 4ST2 Ch. 1.5 - Prob. 5ST2 Ch. 1.5 - Prob. 6ST2 Ch. 1.5 - Prob. 7ST2 Ch. 1.5 - Prob. 8ST2 Ch. 1.5 - Prob. 9ST2 Ch. 1.5 - Prob. 10ST2 Ch. 1.5 - Prob. 11ST2 Ch. 1.5 - Prob. 12ST2 Ch. 1 - Prob. 1CR Ch. 1 - Prob. 2CR Ch. 1 - Prob. 3CR Ch. 1 - Prob. 4CR Ch. 1 - Prob. 5CR Ch. 1 - Prob. 6CR Ch. 1 - Prob. 7CR Ch. 1 - Prob. 8CR Ch. 1 - Prob. 9CR Ch. 1 - Prob. 10CR Ch. 1 - Prob. 11CR Ch. 1 - Prob. 12CR Ch. 1 - Prob. 13CR Ch. 1 - Prob. 14CR Ch. 1 - Prob. 15CR Ch. 1 - Prob. 16CR Ch. 1 - Prob. 17CR Ch. 1 - Prob. 18CR Ch. 1 - Prob. 19CR Ch. 1 - Prob. 20CR Ch. 1 - Prob. 1CT Ch. 1 - Prob. 2CT Ch. 1 - Prob. 3CT Ch. 1 - Prob. 4CT Ch. 1 - Prob. 5CT Ch. 1 - Prob. 6CT Ch. 1 - Prob. 7CT Ch. 1 - Prob. 8CT Ch. 1 - Prob. 9CT Ch. 1 - Prob. 10CT Ch. 1 - Prob. 11CT Ch. 1 - Prob. 12CT Ch. 1 - Prob. 13CT Ch. 1 - Prob. 14CT Ch. 1 - Prob. 15CT Ch. 1 - Prob. 16CT Ch. 1 - Prob. 17CT Ch. 1 - Prob. 18CT Ch. 1 - Prob. 19CT Ch. 1 - Prob. 20CT Ch. 1 - Prob. 21CT Ch. 1 - Prob. 22CT Ch. 1 - Prob. 23CT Ch. 1 - Prob. 24CT

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