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