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Geometric Concepts and Definitions
Mathematical System: Undefined Terms, axioms, definitions, theorems
Euclid (300 BCE) Geometry
undefined terms points P, Q, R, A, B, “no size”
AB , straight, collinear Line Segment AB , midpoint, bisect
lines
planes flat, half-planes
Ray (half-line) AB
Line
A line segment consists of two points on a line and all the points between them. The line segment with
endpoints A and B is denoted by AB .
A point on a line partitions the line into three disjoint sets: the point and two half-lines.
A ray consists of a point on a line and all the points in one of the half-lines determined by the point.
Angle Measurements
An angle is formed by the union of two rays, with a common endpoint. This endpoint is called the vertex,
and the rays are called the sides of the angle.
Degrees, minutes, seconds 360 - one full revolution
“Acute angle” < 90 = “right angle” < “obtuse angle” < 180 = “straight angle” < “reflex angle”
Complementary angles sum to 90
Supplementary angles sum to 180
Adjacent angles share a common side.
An exterior angle of a polygon is formed by the extension of one side thought a vertex of the polygon and
the other side of the polygon through that vertex.
Perpendicular lines meet to form right angles
Parallel lines are lines in a plane that do not meet.
Two lines are parallel if and only if alternate interior angles are equal.
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A circle is the set of all points in a plane that are equidistant from a fixed
The radius is a line segment from appoint on the circle to the center.
A chord is a line segment whose endpoints are both on the circle.
A diameter is a chord that passes through the center.
A tangent is a line that intersects the circle is exactly one point.
The circumference is the distance around the circle.
A disk is the union of a circle and its interior.
point, called the center.
chord
diameter
radius
tangent