SAT Math : Transformation
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Example Question #691 : Geometry
Refer to the above diagram. The plane containing the above figure can be called Plane .
True
False
False
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.
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 #1544 : Basic Geometry
Refer to the above diagram:
True or false: may also called .
False
True
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.
Example Question #691 : Sat Mathematics
Refer to the above diagram.
True or false: and comprise a pair of vertical angles.
False
True
False
By definition, two angles comprise a pair of vertical angles if
(1) they have the same vertex; and
(2) the union of the two angles is exactly a pair of intersecting lines.
In the figure below, and are marked in green and red, respectively:
While the two angles have the same vertex, their union is not a pair of intersecting lines. The two angles are not a vertical pair.
Example Question #692 : Sat Mathematics
Refer to the above diagram.
True or false: and comprise a linear pair.
False
True
False
By definition, two angles form a linear pair if and only if
(1) they have the same vertex;
(2) they share a side; and,
(3) their interiors have no points in common.
In the figure below, and are marked in green and red, respectively:
The two angles have the same vertex and share no interior points. However, they do not share a side. Therefore, they do not comprise a linear pair.
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