Prin. Math - Intro to Geometry

Collinear Points

Points that lie on the same straight line.

Line Segment

A part of a line bounded by two endpoints.

Closed Segment

A segment that includes both endpoints.

Open Segment

A segment that excludes its endpoints.

Ray

A part of a line that begins at one endpoint and extends infinitely in one direction.

Axiom

A statement accepted as true without proof.

Theorem

A statement proven using definitions, postulates, and previously proven theorems.

Point

A location in space with no size or dimension.

Line

An infinite set of points extending in two directions.

Intersecting Lines

Lines that cross at a single point.

Skew Lines

Lines that do not intersect and are not parallel because they are in different planes.

Parallel Lines

Lines that never meet and are always the same distance apart.

Perpendicular Lines

Lines that intersect at a right angle (90°).

Intersecting Planes

Two planes that meet along a line.

Parallel Planes

Planes that do not intersect and are always the same distance apart.

Angle

The figure formed by two rays sharing a common endpoint (vertex).

Acute Angle

An angle measuring greater than 0° and less than 90°.

Obtuse Angle

An angle measuring more than 90° but less than 180°.

Side

A line segment that forms part of a shape or figure.

Vertex

The common endpoint of two rays or sides of a shape.

Interior of an Angle

The region between the two rays that form an angle.

Adjacent Angles

Two angles that share a common side and vertex but do not overlap.

Degree

A unit used to measure the size of an angle.

Minute

A subdivision of a degree; 1° = 60′.

Second

A subdivision of a minute; 1′ = 60″.

Reflex Angle

An angle measuring more than 180° but less than 360°.

Straight Angle

An angle measuring exactly 180°.

Right Angle

An angle measuring exactly 90°.

Supplementary Angles

Two angles whose measures add up to 180°.

Complementary Angles

Two angles whose measures add up to 90°.

Circle

A set of points in a plane that are all the same distance from a fixed point called the center.

Chord

A line segment joining two points on a circle.

Diameter

A chord that passes through the center of the circle.

Radius

A line segment from the center of the circle to a point on the circle.

Central Angle

An angle whose vertex is the center of the circle.

Circumference

The distance around a circle.

Arc

A portion of the circumference of a circle.

Major Arc

An arc greater than a semicircle (more than 180°).

Minor Arc

An arc smaller than a semicircle (less than 180°).

Curve

A continuously bending line without angles.

Simple Curve

A curve that does not cross itself.

Closed Curve

A curve that forms a complete loop.

Polygon

A closed figure made of straight line segments.

Convex Polygon

A polygon where all interior angles are less than 180° and no vertices point inward.

Concave Polygon

A polygon with at least one interior angle greater than 180°.

Congruent Figures

Figures that have the same size and shape.

Regular Polygon

A polygon that is both equilateral and equiangular.

Right Triangle

A triangle with one right angle.

Acute Triangle

A triangle with all angles less than 90°.

Obtuse Triangle

A triangle with one angle greater than 90°.

Scalene Triangle

A triangle with all sides of different lengths.

Isosceles Triangle

A triangle with at least two equal sides.

Equilateral Triangle

A triangle with all sides equal.

Trapezoid

A quadrilateral with at least one pair of parallel sides.

Kite

A quadrilateral with two distinct pairs of adjacent sides equal.

Parallelogram

A quadrilateral with both pairs of opposite sides parallel and equal.

Rectangle

A parallelogram with four right angles.

Rhombus

A parallelogram with all sides equal in length.

Square

A parallelogram with four equal sides and four right angles.

Turn Symmetry

A figure that matches itself after a rotation less than 360°.

Line Symmetry

A figure that can be folded along a line so both halves match.

Point Symmetry

A figure that looks the same after a 180° rotation.

Transversal

A line that crosses two or more other lines at distinct points.

Alternate Interior Angles

Angles formed on opposite sides of a transversal inside parallel lines.

Alternate Exterior Angles

Angles formed on opposite sides of a transversal outside parallel lines.

Corresponding Angles

Angles in the same position at each intersection of a transversal with parallel lines.

Vertical Angles

Opposite angles formed by two intersecting lines; they are congruent.

Polyhedron

A solid with flat polygonal faces, straight edges, and vertices.

Face

A flat surface of a polyhedron.

Vertice

The point where edges of a solid meet (plural

Edge

A line segment where two faces of a solid meet.

Sphere

A set of all points in space at a fixed distance from a center point.

Cone

A solid with a circular base and a vertex not in the base plane.

Pyramid

A solid with a polygonal base and triangular faces meeting at a vertex.

Prism

A solid with two parallel, congruent bases connected by rectangular faces.

Base

The surface a solid figure stands on or is used as a reference face.

Cylinder

A solid with two parallel circular bases connected by a curved surface.

Net

a pattern used to construct a polyhedron

Euler’s Formula 

V + F - E = 2

Measure of each interior angle

180(n-2)/n