CHAPTER 13 SHORT ANSWER
Ways to determine a plane
2 non-collinear pts, a line and a pt not on the line, 2 int. lines, 2 parallel lines
At a given point on a line, how many lines can be drawn perpendicular to the given line?
Infinitely many
Do two oblique lines determine a plane?
Yes
(A,S,N) Two lines perpendicular to the same plane are parallel
always
If a line is perpendicular to one of two parallel lines, then...
it is perpendicular to the other
If a plane is perpendicular to one of two parallel planes, then
it is perpendicular to the other
The intersection of two planes is always a...
line
Do a point and a line determine a plane?
no; point must not be on line
Do three points determine a line?
no; points must be non-collinear
If a line is perpendicular to one of two parallel planes it is...
perpendicular to the other
Two lines that are noncoplanar are called...
skew
If two planes are parallel to the same plane, then
they are parallel
If two planes are perpendicular to the same line, then
they are parallel
Do two intersecting lines determine a plane?
yes
(A,S,N) If 2 lines are parallel to same plane, then they are parallel to each other.
Sometimes
(A,S,N) If two lines do not intersect, then they are parallel
Sometimes
(A,S,N) Two planes parallel to the same line are parallel
Sometimes
In 3D space, what is the locus of points that are equidistant from a given line?
A cylinder that is infinite
In 3D space, what is the locus of points equidistant from a given segment?
A cylinder with 2 hemispheres at each end
In 3D space what is the locus of points equidistant from two given points?
A plane that is the perpendicular bisector of the segment connecting the points
In 3D space, what is the locus of points equidistant from a given point?
A sphere centered around a given point
(A,S,N) 2 lines perpendicular to a plane are parallel
Always
(A,S,N) If 2 lines are perp to same plane, then they are parallel to each other.
Always
(A,S,N) If A, B, and C are noncoplanar, AB perp to BC, and AB perp to BD, then AB is perp to the plane det by B, C, and D.
Always
(A,S,N) If a line is oblique to a plane, it is perpendicular to exactly one line in the plane
Always
(A,S,N) If a line perpendicular to the plane of a circle has its foot at the center of a circle, then a given point on that line is equidistant from every point on that circle.
Always
(A,S,N) If line AB is perp to plane n and plane n is parallel to plane m, then AB is perp to plane m.
Always
(A,S,N) If plane n perp line AB and AB parallel to line CD, plane n perp to CD.
Always
(A,S,N) If plane n perp line AB and AB perp line CD, n is parallel to CD.
Always
If a line is perpendicular to one of two parallel planes, then it is perp to the other
Always
If a plane is perpendicular to one of two parallel planes it is perpendicular to the other
Always
If two lines are perpendicular to the same line they are parallel
Always
If two planes are parallel to the same plane they are parallel
Always
If two planes are perpendicular to the same line they are parallel
Always
(T/F) If a line and a plane are parallel, then every line in the plane is parallel to the given line
False
(T/F) If a line is perpendicular to a line in a plane, it is perpendicular to the plane
False
(T/F) If a line is perpendicular to a line in a plane, then it is perpendicular to the plane
False
(T/F) If a line is perpendicular to a plane, it is perpendicular to every line in the plane
False
(T/F) If a line is perpendicular to a plane, then it is perpendicular to every line in the plane.
False
(T/F) If a line lies in a plane, then a line parallel to the line is parallel to the plane.
False
(T/F) If a plane contains one of two skew lines, it contains the other
False
(T/F) If a plane intersects two intersecting planes, then the lines of intersection are parallel
False
(T/F) If two lines are on parallel planes, then the lines are parallel
False
(T/F) If two parallel lines lie in different planes, the planes are parallel
False
(T/F) If two planes are parallel to the same line, then they are parallel to each other
False
(T/F) In space (3-D), two lines perpendicular to the same line are parallel
False
(T/F) In space, 2 lines perpendicular to the same line are parallel
False
(T/F) It is possible for two planes to intersect at a point
False
(T/F) Three parallel lines are coplanar
False
(T/F) Two lines must either intersect or be parallel
False
(T/F) Two lines parallel to the same plane are oblique
False
(T/F) Two lines perpendicular to the same line are parallel
False
(T/F) 2 lines must either intersect or be parallel
False
(T/F) A line that is perpendicular to a horizontal line is a vertical line
False
(T/F) Any two lines either intersect or are parallel
False
(T/F) Every four-sided figure is a plane figure
False
(A, S, N) If two lines are skew, then they lie in the same plane
Never
(A,S,N) 3 collinear points determine a plane
Never
(A,S,N) Skew lines are coplanar
Never
(A,S,N) Two planes intersect at a point
Never
Do two skew lines determine a plane?
No
At a given point on a plane, how many lines can be drawn perpendicular to the plane?
One
If two lines are perpendicular to the same plane they are...
Parallel
If two planes are parallel to the same plane they are...
Parallel to each other
If a plane is perpendicular to one of two parallel lines it is...
Perpendicular to the other
(A, S, N) Planes that contain two skew lines are parallel.
Sometimes
(A,S,N) If 2 lines are parallel to same plane, perp to each other.
Sometimes
2 planes are parallel if...
They do not intersect
A line and a plane are parallel if...
They do not intersect
2 lines are skew if...
They do not intersect and are not coplanar
(T/F) A triangle is a plane figure
True
(T/F) If a line and a plane never meet, they are parallel
True
(T/F) If a line intersects a plane, then there is at least one line in the plane that is perpendicular to the given line
True
(T/F) If a line is perpendicular to two planes, the planes are parallel.
True
(T/F) If a plane and a line not in the plane are each perpendicular to the same line, then they are parallel to each other.
True
(T/F) If a plane intersects two parallel planes, then the lines of intersection are parallel
True
(T/F) If two lines are parallel, then every plane containing exactly one of the lines is parallel to the other line
True
(T/F) If two points of a line lie on a plane, then the entire line lies on the plane
True
(T/F) In a plane (2-D), two lines perpendicular to the same line are parallel
True
(T/F) In a plane, 2 lines perpendicular to the same line are parallel
True
(T/F) Three distinct points are coplanar
True
(T/F) Two lines perpendicular to the same plane are parallel
True
(T/F) Two perpendicular lines determine a plane
True
