Honors Geometry Definitions

Point

A precise location in space that has no size, width, length, or depth (zero-dimensional)

Line

A straight, continuous arrangement of infinitely many points that extends forever in two opposite directions with no thickness

Plane

A flat surface made up of points that extends infinitely in all direction with no thickness (two-dimensional)

Line segment

a part of a line that consists of two endpoints and all the points between them

Ray

A part of a line that starts at one endpoint and extends forever in one direction

Collinear

Points that lie on the same line

Coplanar

Points or figures that lie in the same plane

Angle

A figure formed by two rays or line segments that share a common endpoint called the vertex

Midpoint

The point on a line segment that divides the segment into two equal (congruent) parts

Angle Bisector

A ray that divides an angle into two congruent (equal) smaller angles

Complementary Angles

Two angles whose measures add up to a sum of 90 degrees

Supplementary Angles

Two angles whose measure add up to a sum of 180 degrees

Perpendicular Lines

Two lines that intersect or line segments that touch to form a right angle (90)

Parallel Lines

Coplanar Lines (or segments) that never intersect, no matter how far they extend

Segment Addition Postulate

If point A, B, and C are collinear, then AB + BC = AC

Angle Addition Postulate

If point D lies in the interior of <ABC, then the measure of the two smaller adjacent angles equals the measure of the total angle. (m<ABD + m<DBC = m<ABC)

Congruence Notation

Used to show that two geometric figures have the exact same shape and size (= with Spanish mark)

Equality Notation

Used strictly for numerical values, such as lengths of segments or degree measures of angles (e.g. AB = CD)

Polygon

A closed, flat (two-dimensional) geometric figure formed by three or more straight line segments connected end-to-end

Convex Polygon

A polygon where no internal angles are greater than 180 degrees, meaning all vertices point outward and no diagonals fall outside the shape.

Concave Polygon

A polygon with at least one interior angle greater than 180 degrees, causing the shape to look like it ‘caves’ in.

Equilateral polygon

A polygon in which all sides are equal in length (Rhombus)

Equilateral polygon

A polygon in which all interior angles are equal in measure (rectangle to hexagons)

Equiangular polygon

A polygon in which all interior angles are equal in measure

Regular polygon

A polygon that is simultaneously equilateral (all sides equal) and equiangular (all angles equal)

Acute Triangle

A triangle in which all three interior angles are acute (measuring strictly less than 90)

Right Triangle

A triangle that contains exactly one right angle (measuring exactly 90)

Obtuse Triangle

A triangle that contains exactly one obtuse angle (measuring strictly between 90 and 180 degrees)

Equilateral Triangle

A triangle with three congruent sides (and consequently, three congruent 60 interior angles)

Isosceles Triangle

A triangle with at least two congruent sides

Scalene Triangle

A triangle in which all three sides have completely different lengths (and all three angles have different measures)

Parallelogram

A four-sided polygon with two pairs of parallel opposite sides

Rectangle

A parallelogram featuring four right angles (90). It is an equiangular quadrilateral

Rhombus

A parallelogram featuring four congruent sides. It is an equilateral quadrilateral

Square

A regular quadrilateral featuring four congruent sides and four right angles. It is simultaneously a rectangle and a rhombus

Trapezoid

A quadrilateral with exactly one pair of parallel opposite sides

Kite

A quadrilateral with two distinct pairs of consecutive, congruent sides that are equal in length

Inductive Reasoning

Logical movement, specific observations, looking for patterns for a broad generality or theory. From specific to general. Making an educated guess or general rule based on specific patterns or observations. The analyzing of data to make a general conclusion.

Deductive Reasoning

From general to specific. Start with theory and run tests for specific cases, guarantees truth of conclusion.

Concurrent lines

three or more straight lines that cross or intersect at the exact, same single point

Congruent

Two figures that have the exact same size and shape