Geometry Unit 1

Definitions

Point

That which has no part

Line

A line is a limitless, breadthless length

Collinear

A set of points are collinear if they all lie on the same line

Intersect, Intersection

Two or more figures intersect if at least one point is on them all. The intersection of two or more figures is the set of points on them all

Segment

A segment is two points on a line and all points on that line between them

Ray

A ray is a point on a line and all points on a given side

Midpoint

The midpoint of a line segment is the point in its interior that divides it into a pair of equal sub-segments. In symbols: if C is the midpoint of segment AB, then C lies between A and B and AC=BC

Angle

an angle is a pair of rays that share an endpoint in common

Angle Side

An angle is composed of a pair of coterminal rays. Each of those two rays is a side of the angle

Angle Vertex

The vertex of an angle is the point of intersection of its two sides

Degree

When a ray completes one complete rotations about its endpoint, it sweeps out 360 degrees. A degree is 1/360th of one complete rotation of a ray about its endpoint

Angle Measure

The measure of an angle is the number of degrees through which one side must rotate to coincide with the other. Two measures are possible for all angles that don’t measure 180 degrees. We choose the smaller unless instructed otherwise.

Angle Bisector

An angle bisector is a ray from the angle’s vertex through its interior that divides it into a pair of equal sub-angles. In symbols: if ray BP is the bisector of angle ABC and measure of angle ABP=measure of angle CBP

Right Angle

An angle is right when it measures 90 degrees

Straight Angle

An angle is straight when its two sides form a line (Note that the definition does not say what straight angles measure. Yes, they measure 180 degrees, but that’s a postulate not a definition)

Opposite Rays

Two rays are opposite when they are co-terminal and together they form a line

Acute Angle

An angle is acute when it measures less than 90 degrees

Obtuse Angle

An angle is obtuse when its measure is greater than 90 degrees and less than 180 degrees

Reflex Angle

An angle is reflex when it measures greater than 180 degrees

Adjacent Angles

Two angles are adjacent when they share a side in common and their interiors do not overlap.

Vertical Angles

Two angles are vertical when they are non-adjacent angles with a common vertex in which their sides form two lines.

Linear Pair

Two angles form a linear pair when they are adjacent and their non-common sides form a line

Complementary

Two angles are complementary when the sum of their measures is 90 degrees

Supplementary

Two angles are supplementary when the sum of their measures is 180 degrees

Perpendicular

Two lines are perpendicular when they form a right angle (NOTE the definition does NOT say that perpendicular lines form four right angles. That’s true, but it’’s not part of the definition. It’s a theorem!)

Polygon

A polygon is composed of line segments called sides. Each side intersects precisely two others: one at one of it’s endpoints, and the other at the other. Adjacent sides are non-collinear.

Polygon Side

The sides of a polygon are the line segments of which it is composed

Polygon Vertex

The vertices of a polygon are the points at which its sides intersect

Diagonal

A diagonal is a segment that joins a pair of non-adjacent vertices in a polygon

Concave

A polygon is concave if at least one segment that joins points in its interior passes outside the polygon.

Convex

A polygon is convex if it is not concave

Equilateral

A polygon is equilateral if all its sides have the same length

Equiangular

A polygon is equiangular if all its angles have the same measure

Regular

A polygon is regular if it is both equilateral and equiangular

Irregular

A polygon is irregular if it is not regular

Postulate

An unproven self-evident assumption

Greater Than

One quantity is greater than another when it is that other plus some positive quantity

Less Than

One quantity is less than another when it is that other minus some positive quantity