Geometry

A plane is an undefined term. We can describe it as

a surface such that if any two points in the surface are joined by a line, then the line lies entirely in the surface. (definition)

If points, lines, segments lie in the same plane, we call them … If they do not lie in the same plane, they are …

coplanar; not coplanar (definition)

If a line passes through two points that lie in a plane, then the line lies…

in the plane (postulate)

If a line intersects a plane not containing it, then they intersect at…

one point (postulate)

If two planes intersect, then their intersection is…

one line (postulate)

What are the ways to determine a plane?

3 non-collinear points, a line and a point not on the line, two intersecting lines

A line is perpendicular to a plane if…

it is perpendicular to every line in the plane that passes through its foot. (definition)

If a line is perpendicular to … then it is perpendicular to the plane.

at least two distinct lines that lie in a plane and pass through its foot (theorem)

Given a plane and a point on the plane, there is … passing through the given point that is perpendicular to the plane.

exactly one line (postulate)

Given a plane and a point not on the plane, there is … passing through the given point that is perpendicular to the plane.

exactly one line (postulate)

A line is … to a plane if it intersects the plane at exactly one point and is not perpendicular to the plane.

oblique (definition)

Law of Trichotomy

For real numbers, exactly one of the following is true:
a<b, a=b, a>b

A …. is a line that intersects two lines in two distinct points.

transversal (definition)

Two … lines are parallel if …

coplanar, they do not intersect (definition)

What is the format for proving lines parallel because of pairs of angles?

If two lines are cut by a transversal and they form a pair of … angles, then they are parallel.

Through a point not on a given line, there exists … that is parallel to the given line.

one unique line (postulate, specifically the Parallel Postulate)

What are each of the undefined terms?

Point, line, plane

A … has neither length nor width but indicates a position. We represent it with a dot.

point

A … has no width and can be extended as far as desired in either direction.

line

If 2 or more points belong to the same … they are said to be …

line, collinear

If 3 or more lines contain the same … they are said to be …

point, concurrent

If point B is between A and C, then A, B, and C are distinct … points and …

collinear, AB+BC=AC

Points B and C are said to be on the same side of point A if …

A, B, and C are distinct collinear points and A is not between B and C.

A line segment is a set of … points of a line and all the points … them.

2, between

A … is a set of points consisting of a fixed point of a line and all the points of that line on the … of the fixed point.

ray, same side

… are two rays of the same line that have a … and no other point in …

Opposite rays, common endpoint, common

An … is a set of points consisting of a union of two … not lying on the same line that have a common …

rays, endpoint

A point P lies in the … of an angle if there exist two points, one on each …, neither at the … such that the point P is between said two points.

interior, side, vertex

Congruent line segments are segments that are …

equal in length

Congruent angles are angles that are …

equal in measure

The … of a line segment is a point of the line segment such that the two segments formed are …

midpoint, congruent

The trisection points of a line segment are the … points of the line segment such that the … segments formed are …

2, 3, congruent

A segment bisector is a line, line segment, or ray that intersects the line segment at its …

midpoint

A right angle is angle measuring …

90 degrees

An acute angle is an angle measuring

>0 degrees and <90 degrees

Anobtuse angle is an angle measuring …

>90 degrees and <180 degrees

Complementary angles are two angles the sum of whose measures is …

90 degrees

Supplementary angles are two angles the sum of whose measures is …

180 degrees

Two lines are said to intersect if they have a … in common

point

Perpendicular lines are two lines that … and form …

intersect, right angles

If two lines in the same plane do not … then they are parallel.

intersect

An angle bisector is the … whose endpoint is the … of the angle and that divides it into two … angles

ray, vertex, congruent

Angle trisectors are the … whose common endpoint is the… of the angle and that divide it into … angles

rays, vertex, 3 congruent

The … of two objects is the set of all points that are contained in at least one of the two objects.

union (∪)

The … of two objects is the set of all points that are contained in at least one of the two objects.

intersection (∩)