Geometry: Undefined Terms, Angles, and Line Relationships

Undefined Terms

Words that do not have a formal definition, but there is agreement about what the words mean. There are 3 undefined terms in geometry.

Point

Is a location. Has neither shape nor size. It is represented by a dot.

Line

Has no thickness or width. It is represented by a straight path of an infinite # of points with 2 arrowheads. There is exactly one line through any 2 points.

Plane

Has two dimensions. It is a flat surface that extends without end. It is modeled by a parallelogram-shaped figure.

Defined Terms

Terms that can be described using known words (point, line, and plane).

Space

A boundless, 3-dimensional set of all points. Space can contain lines and planes.

Collinear Points

Points that lie on the same line.

Coplanar Points

Points that lie on the same plane. There must be at least 3 noncollinear points to determine a plane.

Intersection

The set of points that two or more geometric figures have in common.

Segment (or Line Segment)

Part of a line that consists of two points, called the endpoints, and all the points on the line that are between the endpoints.

Distance Between 2 Points

The absolute value of the difference of the coordinates of the points. PQ = |x1 - x2| = |x2 - x1|.

Between

When three points lie on a line (collinear), you can say that one point is between the other two.

Postulate (Axiom)

A rule that is accepted without proof.

Geometric Construction

A geometric drawing that uses a limited set of tools, usually a compass and straightedge.

Congruent Segments

Line segments that have the same length.

Radical Symbol

A number that involves the square root symbol (√).

Ray

Part of a line that consists of a point called an endpoint and all points on the line that extend indefinitely in one direction.

Angle

Consists of two different rays with the same endpoint.

Triangle

A polygon (closed plane figure) with 3 sides.

Right Triangle

A triangle with one right angle (an angle with measure of 90°).

Midpoint

A point that divides a segment into 2 congruent segments.

Segment Bisector

A line, segment or plane that intersects a segment at its midpoint.

Midpoint Formula

If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint M of AB has coordinates ((x1 + x2)/2, (y1 + y2)/2).

Opposite Rays

Rays that share a common endpoint and travel in opposite directions. Make a line.

Sides of an Angle

The rays that form the angle.

Vertex of an Angle

The shared endpoint of the two rays forming the angle.

Degree

Unit of measure for an angle. Results from dividing the distance around a circle into 360 parts (1° = 1/360 of a turn around a circle).

Acute Angle

An angle with a measure between 0° and 90° (0° < m∠A < 90°).

Right Angle

An angle with a measure of 90° (m∠A = 90°).

Obtuse Angle

An angle with a measure between 90° and 180° (90° < m∠A < 180°).

Straight Angle

An angle with a measure of 180° (m∠A = 180°). Formed by opposite rays.

Congruent Angles

Angles that have the same measure.

Angle Bisector

A ray that divides an angle into two congruent angles.

Adjacent Angles

Two angles that share a common vertex and side, but have no common interior points. ('Right next to')

Complementary Angles

Two angles whose measures have the sum of 90°.

Supplementary Angles

Two angles whose measures have the sum of 180°.

Linear Pair

Two adjacent angles whose non-common sides are opposite rays. The angles in a linear pair add to 180°.

Vertical Angles

Two non-adjacent angles formed by two intersecting lines.

Perpendicular

Lines, segments, or rays that form right angles.