Lines - Geometry
Card 0 of 284
Which of the following are the sides of 
?
Which of the following are the sides of
The sides of an angle are two rays, both of which begin at a common vertex. Since the middle letter of the name of this angle is 
, 
is the common endpoint; therefore, the name of each ray starts with 
. This makes 
and 
the correct choice.
Note that 
and 
cannot be correct: these are line segments.
The sides of an angle are two rays, both of which begin at a common vertex. Since the middle letter of the name of this angle is
Note that
Compare your answer with the correct one above
A ray is different from a line in that
A ray is different from a line in that
A ray is defined by two points, one that defines the beginning, and the other that defines the direction - this ray goes on forever in whatever direction is defined by that second point
A ray is defined by two points, one that defines the beginning, and the other that defines the direction - this ray goes on forever in whatever direction is defined by that second point
Compare your answer with the correct one above
Which of the following is not a side of 
?
Which of the following is not a side of
The two sides of an angle are the two rays that compose it. Each of these rays begins at the vertex and proceeds out from there. In naming a ray, we always begin with the letter of the endpoint (where the ray starts) followed by another point on the ray in the direction it travels. Since the vertex of the angle is the endpoint of each ray and our vertex is 
, each of our rays must begin with 
. Only 
fails to do so.
The two sides of an angle are the two rays that compose it. Each of these rays begins at the vertex and proceeds out from there. In naming a ray, we always begin with the letter of the endpoint (where the ray starts) followed by another point on the ray in the direction it travels. Since the vertex of the angle is the endpoint of each ray and our vertex is
Compare your answer with the correct one above
How does a ray differ from a line segment?
How does a ray differ from a line segment?
Line segment: part of a line that has two distinct end points.
Ray: portion of a line with one end point, where the other end of the line continues to infinity.
Line segment: part of a line that has two distinct end points.
Ray: portion of a line with one end point, where the other end of the line continues to infinity.
Compare your answer with the correct one above
Refer to the above diagram.
True or false: 
and 
refer to the same line segment.
Refer to the above diagram.
True or false:
The two letters in the name of a line segment are its endpoints in either order. Therefore, 
is the segment with endpoints 
and 
; consequently, it can also be called .
The two letters in the name of a line segment are its endpoints in either order. Therefore,
Compare your answer with the correct one above
Refer to the above diagram.
True or false: 
, 
, and 
are collinear points.
Refer to the above diagram.
True or 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 such a line exists.
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.
Compare your answer with the correct one above
Refer to the above diagram. The plane containing the above figure can be called Plane 
.
Refer to the above diagram. The plane containing the above figure can be called Plane
A plane can be named after any three points on the plane that are not on the same line. As seen below, points 
, 
, and 
are on the same line.
Therefore, Plane 
is not a valid name for the plane.
A plane can be named after any three points on the plane that are not on the same line. As seen below, points
Therefore, Plane
Compare your answer with the correct one above
Refer to the above diagram.
True or false: Quadrilateral 
can also be called Quadrilateral 
.
Refer to the above diagram.
True or false: Quadrilateral
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.
A quadrilateral is named after its four vertices in consecutive order, going clockwise or counterclockwise. Quadrilateral
Compare your answer with the correct one above
Refer to the above diagram:
True or false: 
may also called 
.
Refer to the above diagram:
True or 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.
A line can be named after any two points it passes through. The line
The line does not pass through
Compare your answer with the correct one above
True or false: The plane containing the above figure can be called Plane 
.
True or false: The plane containing the above figure can be called Plane
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.
A plane can be named after any three points on the plane that are not on the same line.
Plane
Compare your answer with the correct one above
Refer to the above diagram.
True or false: can also be called 
.
Refer to the above diagram.
True or false:
A line segment has two letters in its name, each of which is an endpoint. is therefore the segment marked in red below.
is not a valid name, since 
is not an endpoint of the segment.
A line segment has two letters in its name, each of which is an endpoint.
Compare your answer with the correct one above
Refer to the above diagram.
True or false: can also be called 
.
Refer to the above diagram.
True or false:
A segment is named with only two letters, each of which is an endpoint. 
is not a valid name.
A segment is named with only two letters, each of which is an endpoint.
Compare your answer with the correct one above
Refer to the above diagram.
True or false: 
and 
refer to the same ray.
Refer to the above diagram.
True or false:
A ray is named with two letters, the first of which is an endpoint and the second of which is any other point the ray passes through. 
is a ray with endpoint 
, and 
is a ray with endpoint 
; 
and 
are therefore not the same ray.
A ray is named with two letters, the first of which is an endpoint and the second of which is any other point the ray passes through.
Compare your answer with the correct one above
Refer to the above diagram.
True or false: 
and 
refer to the same ray.
Refer to the above diagram.
True or false:
A ray is named with two letters, the first of which is an endpoint and the second of which is any other point the ray passes through. 
has its endpoint at 
and passes through 
; it is the ray marked in red in the figure below:
The ray also passes through Point 
, so the ray can also be called 
.
A ray is named with two letters, the first of which is an endpoint and the second of which is any other point the ray passes through.
The ray also passes through Point
Compare your answer with the correct one above
Refer to the above diagram.
True or false: 
, 
, and are collinear points.
Refer to the above diagram.
True or 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.
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
Therefore, the three points are not collinear.
Compare your answer with the correct one above
Refer to the above figure.
True or false: 
and 
comprise a pair of opposite rays.
Refer to the above figure.
True or 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.
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,
Compare your answer with the correct one above
Refer to the above figure.
True or false: 
and 
comprise a pair of opposite rays.
Refer to the above figure.
True or 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.
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.
As it turns out, the two rays are one and the same.
Compare your answer with the correct one above
Refer to the above figure.
True or false: 
and 
comprise a pair of opposite rays.
Refer to the above figure.
True or 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 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.
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.
The union of the two rays is a line. Both criteria are met, so the rays are indeed opposite.
Compare your answer with the correct one above
If 
, 
, and 
, what is the measure, in degrees, of 
?
If 
The question states that 
. The alternate interior angle theorem states that if two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent; therefore, we know the following measure:
The sum of angles of a triangle is equal to 180 degrees. The question states that 
; therefore we know the following measure:
Use this information to solve for the missing angle: 
The degree measure of a straight line is 180 degrees; therefore, we can write the following equation:
The measure of 
is 148 degrees.
The question states that 
The sum of angles of a triangle is equal to 180 degrees. The question states that 
Use this information to solve for the missing angle:
The degree measure of a straight line is 180 degrees; therefore, we can write the following equation:
The measure of 
Compare your answer with the correct one above
In the following diagram, lines 
and 
are parallel to each other. What is the value for 
?
In the following diagram, lines
When two parallel lines are intersected by another line, the sum of the measures of the interior angles on the same side of the line is 180°. Therefore, the sum of the angle that is labeled as 100° and angle y is 180°. As a result, angle y is 80°.
Another property of two parallel lines that are intersected by a third line is that the corresponding angles are congruent. So, the measurement of angle x is equal to the measurement of angle y, which is 80°.
When two parallel lines are intersected by another line, the sum of the measures of the interior angles on the same side of the line is 180°. Therefore, the sum of the angle that is labeled as 100° and angle y is 180°. As a result, angle y is 80°.
Another property of two parallel lines that are intersected by a third line is that the corresponding angles are congruent. So, the measurement of angle x is equal to the measurement of angle y, which is 80°.
Compare your answer with the correct one above