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Geometry: Planes: CH. 6
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Terms in this set (85)
Skew lines are parallel.
never
two lines that do not intersect are skew.
sometimes
through a point outside a plane there are infinitely many planes parallel to that plane.
never
two lines perpendicular to the same plane are parallel to esch other
always
if a plane and a line not in that plane are perpedicular to the same line, they are parallel to each other.
always
Two lines perpendicular to a third line are perpendicular to each other
sometimes
If a plane and a line not in that plane are perpendicular to the same plane, they are parallel to each other
always
Two lines parallel to a third line are parallel to each other
always
Two lines parallel to the same plane are parallel to each other
sometimes
Two planes parallel to the same line are parallel to each other
sometimes
Two planes parallel to the same plane are parallel to each other
always
Two lines skew to the same line are skew to each other
sometimes
In a plane, two lines perpendicular to the same line are perpendicular to each other
never
A plane and a line not in that plane which are parallel to the same line are parallel to each other
always
A plane and a line not in that plane which are parallel to the same plane are parallel to each other
always
A line which intersects one of two parallel lines intersects the other also
sometimes
In a plane, a line which intersects one of two parallel lines intersects the other also
always
A plane that cuts one of two parallel lines in one point intersects the other line also
always
A plane that intersects one of two skew lines in one point intersects the other line also
sometimes
Two planes each perpendicular to a third plane are parallel to each other
sometimes
A plane that contacins two sides of a triangle containes the third side also
always
A plane not containing any vertex of a triangle but intersecting two sides of that triangle intersects the third side also
never
Given two skew lines, there exist infinitely many planes parallel to both of the lines
always
Given two skew lines, it is possible to find a plane containing one of the lines and parallel to the other
always
Given two skew lines, there exists a line perpendicular to both of the skew lines
always
Is it possible to actually "see" a geometric point
no
Is it possible to actually "see" a plane figure
no
How many straight lines can be drawn containing one point
infinity
How many straight lines can be drawn containing two points
1
How many straight lines can be drawn containing three noncollinear points
0
How many planes can contain a given point
infinity
How many planes can contain two given points
infinity
How many planes can contain three noncollinear points
1
How many planes can contain a given straight line
infinity
How many planes can contain two intersecting lines
1
How many planes can contain two parallel lines
1
How many planes can contain two skew lines
0
How many planes can contain a line and an external point
1
How many lines are determines by four points, no three of which are collinear
6
How many planes are determined by four points if no three of them are collinear and not all four are coplanar
4
How many planes are determined by three concurrent lines that are not coplanar
3
How many planes are determined by four concurrent lines no three of which are coplanar
6
What is the least number of planes that can enclose a space
4
In a plane, how many lines may be drawn perpendicular to a given line at a point in the line
1
In space, how many lines may be drawn perpendicular to a given line at a point in the line
infinity
If two lines are perpendicular to each other, do they lie in the same plane
yes
Can two oblique lines be parallel
yes
Can two oblique lines intersect each other
yes
Can a line be perpendicular to exactly one line of a plane
yes
Can two oblique lines be perpendicular to each other
yes
Can two skew lines intersect
no
Can two skew lines be perpendicular
no
Can two skew lines be vertical
no
Can two skew lines be horizontal
yes
Is every vertical line also horizontal
yes
Is every horizontal line also vertical
no
If two planes are each parallel to the same line, are they parallel
not neccessarily
If a line intersects one of two parallel planes, will it intersect the other
not necessarily
If two planes are parallel to a third plane, are they parallel to each other
yes
Do two lines each parallel to a plane determine a plane parallel to the given plane
not necessarily
How many concurrent lines may be parallel to a line
0
How many concurrent lines may be parallel to a plane
infinity
How many concurrent planes may be parallel to a line
infinity
How many concurrent planes may be parallel to a plane
0
If a line intersects two skew lines, do all threee lines lie in the same plane
no
If a line is parallel to a plane, is it parallel to several lines in the plane
yes, infinity
If two planes are perpendicular to the same plane, are the planes parallel
not necessarily
If two planes are perpendicular to the same plane, can the planes be parallel
yes
A line can be perpendicular to each of two intersecting line
true
If a line is perpendicaular to two planes, the planes are parallel
true
A line can be perpendicular to two intersecting planes
false
A line can be perpendicular to two skew lines
true
a line and a plane that do not intersect
parallel
parallel planes are planes that do not
intersect
lines that are not coplanar
skew
if plane intersects two parallel planes,
lines of intersection are parallel
if two planes are perp to the same line,
planes parallel to each other
if a line is perp to one of two parallel planes
perp to other plane
if two planes are parallel to the same plane
parallel to each other
if two lines are perp to same plane
parallel to each other
if plane is perp to one of two parallel lines
perp to other
if two lines parallel to the same line
parallel to each other
4 ways to determine a plane
2 intersecting lines, 2 parallel lines, a line and a point not on it, 3 noncollinear points
christmas tree theorem
If a line perp to 2 distict lines in the plane through the foot, then it is perp to plane.
opp christmas tree theorem
a line is perp to a plane if it is perp to every line in the plane through the foot
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