Geometry Problem Solving Drill – 03: Points, Lines, Planes, and Their Relationships
Question No. 1 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 1. If a line intersects line a in one point, then how many points of intersection does it have with
the other lines in this figure?
Question #01
(A)
(B)
(C)
(D)
5
3
4
2
A. Incorrect!
Review the properties of transversals.
Feedback on
Each Answer
Choice
B. Correct!
The line intersects all the parallel lines, each at one point.
C. Incorrect!
Review the properties of transversals.
D. Incorrect!
Review the properties of transversals.
Solution
The line intersects all the parallel lines each at one point because if a line intersects one parallel line, it
intersects all of the lines in the set.
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 2 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 2. Which lines are transversal?
B
C
F
E
H
G
Question #02
K
L
D
A
(A)
(B)
(C)
(D)
AB
AB
AB
AB
and
and
and
and
CD
EF
GH
KL
A. Correct!
Used the definition of transversal.
Feedback on
Each Answer
Choice
B. Incorrect!
Review the definition of a transversal.
C. Incorrect!
Review the definition of a transversal.
D. Incorrect!
Review the definition of a transversal.
Solution
A transversal is any line that intersects a set of lines. The only lines that follow this rule are lines AB and
CD. Therefore, A is the correct answer.
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 3 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 3. What are two lines called if they are neither parallel nor intersecting?
Question #03
(A)
(B)
(C)
(D)
Congruent
Equal
Skew
Collinear
A. Incorrect!
Lines cannot be congruent because their length is infinity.
Feedback on
Each Answer
Choice
B. Incorrect!
Lines cannot be equal because their length is infinity.
C. Correct!
By definition, two lines that are neither parallel nor intersecting are skew lines.
D. Incorrect!
Lines cannot be collinear.
By definition, two lines that are neither parallel nor intersecting are skew lines. Therefore, choice C is
correct.
Solution
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 4 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 4. Point C is collinear with which set of points?
C
D
F
Question #04
A
(A)
(B)
(C)
(D)
(A,
(A,
(A,
(A,
B
F) and (B, F)
B) and (B, F)
F) and (C, D)
F) and (B, D)
A. Incorrect!
Review the definition of collinear points and try again.
Feedback on
Each Answer
Choice
B. Incorrect!
Review the definition of collinear points and try again.
C. Incorrect!
Review the definition of collinear points and try again.
D. Correct!
By definition, collinear points lie on the same line.
Solution
By definition, collinear points lie on the same line. Therefore, choice D is correct.
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 5 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 5. Lines AB, CD, EF, GH, and JK are parallel. Line RS intersects lines GH. Which statement is
true?
Question #05
(A)
(B)
(C)
(D)
RS
RS
RS
RS
is parallel to all the given lines.
does not intersect line EF.
intersects line CD.
and AB are skew lines.
A. Incorrect!
Review the properties of parallel lines and try again.
Feedback on
Each Answer
Choice
B. Incorrect!
Review the properties of parallel lines and try again.
C. Correct!
If a line intersects one of a set of parallel lines, the line intersects all of the lines in the set.
D. Incorrect!
Review the properties of parallel lines and try again.
If a line intersects one of a set of parallel lines, the line intersects all of the lines in the set. Therefore, if
line RS intersects GH then it must intersect CD. Choice C is correct.
Solution
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 6 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 6. How many planes can be passed through three non-collinear points?
Question #06
(A)
(B)
(C)
(D)
Four
Three
Two
One
A. Incorrect!
Review the definition of a plane and try again.
Feedback on
Each Answer
Choice
B. Incorrect!
Review the definition of a plane and try again.
C. Incorrect!
Review the definition of a plane and try again.
D. Correct!
Three non-collinear points create a two-dimensional shape that has length and width, but no thickness.
Solution
Three non-collinear points create a two-dimensional shape that has length and width, but no thickness.
Therefore, choice D is correct.
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 7 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 7. How many planes can be passed through two points?
Question #07
(A)
(B)
(C)
(D)
Infinite
Four
Two
One
A. Correct!
Two points make a line and an infinite number of planes can pass through that one line.
Feedback on
Each Answer
Choice
B. Incorrect!
Review the definition of plane and try again.
C. Incorrect!
Review the definition of plane and try again.
D. Incorrect!
Review the definition of plane and try again.
Solution
Two points make a line and an infinite number of planes can pass through that one line. Therefore,
choice A is correct.
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 8 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 8. Points A, B, and C are on the line MN and points B, E, and F are on the line PQ. Point R is
outside of these lines. Which set of points can be collinear?
Question #08
(A)
(B)
(C)
(D)
A,
A,
B,
R,
B, R
C, R
C, E
E, A
A. Incorrect!
It has already been stated that R is outside of the line containing A and B. Try again.
Feedback on
Each Answer
Choice
B. Incorrect!
It has already been stated that R is outside of the line containing A and C. Try again.
C. Incorrect!
It has already been stated that E is on a line different from the line containing B and C. Try again.
D. Correct!
It is possible that points R, E, and A are collinear since no relationship has been stated between them.
Solution
Choice A: It has already been stated that R is outside of the line containing A and B.
Choice B: It has already been stated that R is outside of the line containing A and C.
Choice C: It has already been stated that E is on a line different from the line containing B and C.
Choice D: It is possible that points R, E, and A are collinear since no relationship has been stated
between them.
The only choice containing points that have not been defined as noncollinear is choice D.
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 9 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 9. How many points are needed to represent a line?
Question #09
(A)
(B)
(C)
(D)
Five
Four
Three
Two
A. Incorrect!
Review the definition of a line.
Feedback on
Each Answer
Choice
B. Incorrect!
Review the definition of a line.
C. Incorrect!
Review the definition of a line.
D. Correct!
By definition, a line is formed by connecting two points and extending beyond each point in both
directions.
By definition, a line is formed by connecting two points and extending beyond each point in both
directions. Therefore, choice D is correct.
Solution
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved
Question No. 10 of 10
Instruction: (1) Read the problem statement and answer choices carefully (2) Work the problems on paper as needed (3)
Pick the answer (4) Go back to review the core concept tutorial as needed.
Question 10. Which group of points represents collinear points?
E
C
Question #10
F
D
B
A
(A) (A, C, D), (E, D, B), (C, D, F), (A, B, F)
(B) (A, C, E), (E, F, B), (C, D, F), (A, B, F)
(C) (A, C, E), (E, D, B), (C, D, F), (A, B, F)
(D) (A, C, E), (E, D, B), (C, D, B), (A, B, F)
A. Incorrect!
Review the definition of collinear points and try again.
Feedback on
Each Answer
Choice
B. Incorrect!
Review the definition of collinear points and try again.
C. Correct!
By definition, collinear points lie in the same line.
D. Incorrect!
Review the definition of collinear points and try again.
By definition, collinear points lie in the same line. The only sets of points that follow this rule are in
choice C.
Solution
RapidLearningCenter.com
© Rapid Learning Inc. All Rights Reserved