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Example Questions
Example Question #1541 : Basic Geometry
Refer to the above figure.
True or false: and
comprise a pair of opposite rays.
False
True
False
Two rays are opposite rays, by definition, if
(1) they have the same endpoint, and
(2) their union is a line.
The first letter in the name of a ray always refers to the endpoint of the ray. Therefore, has its endpoint at
and
has its endpoint at
. The two rays are not opposite rays.
Example Question #1541 : Basic Geometry
Refer to the above figure.
True or false: and
comprise a pair of opposite rays.
True
False
False
The first letter in the name of a ray refers to its endpoint; the second refers to the name of any other point on the ray. and
are rays that have endpoint
and pass through
and
, respectively. Those rays are indicated below in red and green, respectively.
As it turns out, the two rays are one and the same.
Example Question #1541 : Basic Geometry
Refer to the above figure.
True or false: and
comprise a pair of opposite rays.
True
False
True
Two rays are opposite rays, by definition, if
(1) they have the same endpoint, and
(2) their union is a line.
The first letter in the name of a ray refers to its endpoint; the second refers to the name of any other point on the ray. and
both have endpoint
, so the first criterion is met.
passes through point
and
passes through point
;
and
are indicated below in green and red, respectively:
The union of the two rays is a line. Both criteria are met, so the rays are indeed opposite.
Example Question #1541 : Basic Geometry
Refer to the above diagram.
True or false: ,
, and
are collinear points.
True
False
False
Three points are collinear if there is a single line that passes through all three. In the diagram below, it can be seen that the line that passes through and
does not pass through
.
Therefore, the three points are not collinear.
Example Question #1541 : Basic Geometry
Refer to the above diagram.
True or false: ,
, and
are collinear points.
True
False
True
Three points are collinear if there is a single line that passes through all three. In the diagram below, it can be seen that such a line exists.
Example Question #14 : How To Find A Ray
True or false: The plane containing the above figure can be called Plane .
False
True
True
A plane can be named after any three points on the plane that are not on the same line. ,
, and
do not appear on the same line; for example, as can be seen below, the line that passes through
and
does not pass through
.
Plane is a valid name for the plane that includes this figure.
Example Question #1541 : Basic Geometry
Refer to the above diagram.
True or false: Quadrilateral can also be called Quadrilateral
.
True
False
False
A quadrilateral is named after its four vertices in consecutive order, going clockwise or counterclockwise. Quadrilateral is the figure in red, below:
,
,
, and
are not a clockwise or counterclockwise ordering of the vertices, so Quadrilateral
is not a valid name for the quadrilateral.
Example Question #11 : How To Find A Ray
Refer to the above diagram:
True or false: may also called
.
True
False
False
A line can be named after any two points it passes through. The line is indicated in green below.
The line does not pass through , so
cannot be part of the name of the line. Specifically,
is not a valid name.
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