Geometry Fundamentals

Vocabulary practice flashcards generated from lecture notes covering foundational geometry concepts, definitions, postulates, and formulas.

Segment

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

Vertex

The common endpoint of an angle where the sides intersect.

Collinear Points

Points that lie on the same line.

Noncoplanar Lines

Lines that do not lie in the same plane; also known as skew lines.

Concave

Curved inward, not convex; having an outline or surface that curves inward.

Betweenness of Points

For any two points A and C on a line, there is another point B between A and C if and only if A, B, and C are collinear and $AB + BC = AC$.

Congruent

Having the same size and shape.

Theorem

A statement that has been proven.

Line

An undefined term with a straight path, no thickness, extending infinitely far in opposite directions, and containing infinitely many points.

Bisect

To divide a figure into two congruent parts.

Midpoint

A point that divides a segment into two congruent segments.

Measure of an Angle

The smallest amount of rotation about the vertex from one ray to the other, measured in degrees.

Congruent Angles

Angles that have the same measure.

Supplementary Angles

Two angles whose measures have a sum of 180 degrees.

Polygon

A closed figure formed by three or more line segments.

Adjacent Angles

Two angles that share a common vertex and side, but have no common interior points.

Postulate / Axiom

A rule that is accepted without proof.

Angle Addition Postulate

If point B lies in the interior of $\angle AOC$, then $m\angle AOB + m\angle BOC = m\angle AOC$.

Complementary Angles

Two angles whose measures have a sum of 90 degrees.

Segment Bisector

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

Ray

Part of a line that starts at an endpoint and extends infinitely far in one direction.

Intersection

The set of points the figures have in common.

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary.

Linear Pair of Angles

Two adjacent angles whose non-shared rays form a straight angle.

n-gon

A polygon with n sides.

Angle

A figure formed by two rays with a common endpoint.

Construction

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

Angle Bisector

A ray that divides an angle into two congruent angles.

Noncollinear Points

Points that do not lie on the same line.

Distance Formula

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Slope of a Line

Measures how steep a line is.

Point

An undefined term with a location but no size, represented by a dot and named by a capital letter.

Convex Polygon

A polygon where no line that contains a side of the polygon contains a point in the interior of the polygon.

Segment Addition Postulate

If Q is between P and R, then $PQ + QR = PR$.

Perpendicular Lines

Two lines that intersect to form right angles.

Opposite Rays

Two rays that have the same endpoint and go in opposite directions forming a line.

Ruler Postulate

The points on a line can be put into a one-to-one correspondence with the real numbers.

Coplanar Points or Lines

Points or lines that are in the same plane.

Plane

An undefined term described as a flat surface that has no thickness and extends forever.

Congruent Segments

Line segments that have the same length.

Coordinate

The real number that corresponds to a point.

Midpoint Formula

$$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$

Vertical Angles

Two angles whose sides form two pairs of opposite rays.

Noncoplanar Points

Points that are not in the same plane.

Interior Region of an Angle

The region that contains all the points between the sides of the angle.

Exterior Region of an Angle

The region that contains all the points outside the angle.