Concept explainers
(a)
To state: The postulate permits that there are two points R and S in the line k.
(a)
Answer to Problem 20WE
Postulate 5.
Explanation of Solution
Given information:
Consider the statement below:
Parts a through d justify Theorem 1-2. Through a line and point not in the line there is exactly one plane.
Formula used:
The non-collinear points are used.
Calculation:
From Postulate 5, a line contains at least 2 points.
Therefore, line k contains atleast two points R and S.
Hence, the answer is postulate 5.
Conclusion:
The postulate 5 is obtained.
(b)
To check: The one plane X contains the point P, R and S.
(b)
Answer to Problem 20WE
The reason is postulate 7
Explanation of Solution
Given information:
Consider the statement below:
Parts a through d justify Theorem 1-2. Through a line and point not in the line there is exactly one plane.
Formula used:
The non-collinear points are used.
Calculation:
From Postulate 7, through any 3 points there is atleast one plane. Therefore, through points P, R and S there is at least one plane X.
Hence, the answer is postulate 7.
Conclusion:
Through points P, R and S there is at least one plane X.
(c)
To find: The postulate that the plain contains the line k.
(c)
Answer to Problem 20WE
The answer is theorem 1-2.
Explanation of Solution
Given information:
Consider the statement below:
Parts a through d justify Theorem 1-2. Through a line and point not in the line there is exactly one plane.
Formula used:
The non-collinear points are used.
Calculation:
From b. points P, R and S are contained in at least one plane X and from a. line k contains two points R and S.
From Theorem 1-2, through a line and point not in the line there is exactly one plane.
Therefore, X must contain line k by above argument
Hence, the answer is theorem 1-2.
Conclusion:
X must contain line k
(d)
To identify: The postulate that results in contradiction of the given statement.
(d)
Answer to Problem 20WE
The answer is postulate 7
Explanation of Solution
Given information:
Consider the statement below:
Parts a through d justify Theorem 1-2. Through a line and point not in the line there is exactly one plane.
Formula used:
The non-collinear points are used.
Calculation:
From b, points P, R and S are contained in a plane X. From Postulate 7, through any 3 non collinear points there is exactly one plane. Points P, R and S are non-collinear points.
Therefore, X is the unique plane that contains points P, R and S.
Hence, the answer is postulate 7.
Conclusion:
X is the unique plane that contains points P, R and S.
Chapter 1 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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