Chapter 1 Geometry: Points, Lines, Planes, and Angles

Vocabulary flashcards reviewing fundamental geometric concepts, terms, postulates, and theorems from Chapter 1.

Point

An undefined term in geometry that has no size, is represented by a dot, and is named using a capital letter.

Line

An undefined term in geometry that extends in two directions without ending and has no thickness.

Plane

An undefined term in geometry that is a flat surface extending without length and width limits (has no edges).

Collinear Points

Points that all lie on the same line.

Coplanar Points

Points that all lie on the same plane.

Segment

A part of a line consisting of two endpoints and all points between them.

Ray

A part of a line that extends without end in one direction, named by its endpoint and any other point on the ray.

Opposite Rays

Two rays that share a common endpoint and extend in opposite directions to form a line.

Postulate

A statement that is accepted without proof.

Ruler Postulate (Postulate 1)

The points on a line can be paired with real numbers such that the distance between any two points $a$ and $b$ is $|a - b|$.

Segment Addition Postulate (Postulate 2)

A postulate stating that if $B$ is between $A$ and $C$, then $AB + BC = AC$.

Congruent Segments

Segments that have equal lengths.

Midpoint of a Segment

The point that divides a segment into two congruent segments.

Bisector of a Segment

Any line, segment, or ray that intersects a segment at its midpoint.

Angle

A figure formed by two rays with a common endpoint.

Vertex

The common endpoint of the two rays that form an angle.

Sides of an Angle

The two rays that form an angle.

Acute Angle

An angle with a measure between $0^\circ$ and $90^\circ$.

Right Angle

An angle with a measure of exactly $90^\circ$.

Obtuse Angle

An angle with a measure between $90^\circ$ and $180^\circ$.

Straight Angle

An angle with a measure of exactly $180^\circ$.

Angle Addition Postulate (Postulate 4)

A postulate stating that if $B$ is in the interior of $\angle AOC$, then $m\angle AOB + m\angle BOC = m\angle AOC$.

Congruent Angles

Angles that have equal measures.

Adjacent Angles

Two coplanar angles with a common vertex and a common side, but no common interior points.

Bisector of an Angle

A ray that divides an angle into two congruent adjacent angles.

Theorem

A statement in geometry that is proved.

Theorem 1-1

If two lines intersect, then they intersect in exactly one point.

Theorem 1-2

Through a line and a point not on that line, exactly one plane contains them.

Theorem 1-3

If two lines intersect, then exactly one plane contains the lines.

Postulate 5a

A line contains at least two points.

Postulate 5b

A plane contains at least three noncollinear points.

Postulate 5c

Space contains at least four noncoplanar points.

Postulate 6

Through any two points there is exactly one line.

Postulate 7

Through any three noncollinear points there is at least one plane.

Postulate 8

If two points lie in a plane, then the line containing them lies in the plane.

Postulate 9

If two planes intersect, then their intersection is a line.