12 multiple-choice questions, progressively harder.
Which object represents an exact location with no size?
Solution
Correct answer: B
A point represents a location. The dot used to draw it has size, but the geometric point does not.
Which notation names the whole line through distinct points AAA and BBB?
Correct answer: D
The double-ended arrow indicates that the line continues without end in both directions. A bar names a segment, and a single arrow names a ray.
What is the endpoint of PQ→\overrightarrow{PQ}PQ?
Correct answer: A
The first letter names a ray's endpoint. The ray begins at PPP, passes through QQQ, and continues beyond QQQ.
Distinct points J,L,NJ,L,NJ,L,N occur in that order on one line. What is the set of all points shared by rays LJ→\overrightarrow{LJ}LJ and LN→\overrightarrow{LN}LN?
Correct answer: C
Both rays start at LLL, so LLL belongs to both.
They extend in opposite directions along the line.
No other point lies on both rays, so their intersection is only LLL.
Points HHH, JJJ, and KKK all lie on one line. What word describes these three points?
Collinear points belong to one line. The description does not require their spacing or any measurement.
Which information guarantees a unique plane?
The plane foundation requires three noncollinear points. Points all on one line leave many planes possible through that line.
How many lines contain two given distinct points?
The unique-line foundation states that exactly one line contains two distinct points. Distinct means the points are different locations.
What does it mean for points to be coplanar?
Coplanar means lying in one plane. The points may be collinear or noncollinear, so neither a common line nor the absence of a common line defines coplanarity.
Two distinct lines are coplanar and have no common point. How are they related?
Parallel lines are distinct, coplanar lines that do not meet. Skew lines are not coplanar, and perpendicular lines meet.
Which description defines skew lines?
Skew lines are noncoplanar. They neither intersect nor qualify as parallel.
Two distinct intersecting planes share what kind of object?
The plane-intersection foundation says that two distinct planes, if they meet, meet along a line. The distinctness condition excludes coincident planes.
Two planes are coincident. Which statement is correct?
Coincident planes contain exactly the same points. They are one geometric plane, even if named in two ways.
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