Subject: Geometry

Words & Symbols In Geometry

This section will serve as a basic introduction to some of the things you’ll see in geometry – you’ll no doubt have heard many of these terms and seen many of these symbols before, but it’s good to see what we’ll be using, and it’s handy to have a quick guide.

A List of Words Used in Geometry

(More in depth explanations and examples will be covered in subsequent pages!)

The Breakdown

POINTS, LINES AND PLANES

Line
In geometry, the definition of line must be more precise than our everyday use of the word because we also have to deal with rays and segments. A line may be straight or curved, and straight lines continue on past any points upon them. Lines are usually named after their two furthest points.
Ray
A portion of a straight line that begins at a point and continues indefinitely.
Segment
A portion of a straight line with two distinct endpoints, a line with finite length.
Point
A symbol used to show position. Represented by a small dot or a letter.
Endpoint
A point at one end of a segment, or the beginning of a ray.
Midpoint
A point exactly halfway along a segment.
Axis / Axes
A fixed, numbered reference line used in coordinate geometry.
Origin
The point at which two or more axes meet in coordinate geometry.
Vertex
The point where two straight lines, segments or rays meet creating an angle.
Bisect
To bisect is to cross a line or segment at it’s midpoint.
Plane
A two-dimensional form with length and width but no depth or thickness.
Collinear
A set of two or more points is said to be collinear if they lie upon the same line.
Congruent
Segments that have the same length are congruent.


ANGLES

Measure
A word used when talking about the value of an angle. An example might be “The measure of angle X is 120°”.
Right Angle
An angle with a measure of exactly 90°.
Perpendicular
Two lines are perpendicular if the angle which their intersection or meeting point forms is exactly 90°.
Obtuse
An angle with measure greater than 90° and less than 180°.
Acute
An angle with a measure of less than 90°.
Adjacent Angles
Two angles are adjacent if they share the same vertex.
Vertical Angles
Two non-adjacent angles formed by intersecting lines.
Complementary
Angles whose combined total value add to exactly 90°.
Supplementary
Angles whose combined total value add to exactly 180°.


CIRCLES

Chord
A straight line joining any two points on a circle.
Secant
A straight line joining any two points on a circle and continuing beyond those points in both directions.
Arc
A portion of the circumference of a circle between and including two points.
Diameter
A chord that passes through the middle of the circle.
Radius
The straight length or distance between the centre of a circle and a point on its circumference. The radius of a circle is exactly half of that circles diameter. The plural of radius is radii (pronounced ‘ray-dee-eye’).
Circumference
The length around a circle.
Semicircle
An arc measuring exactly half the circumference of a circle. Literally half a circle.
Central Angle
An angle formed by two radii of the same circle (not two overlapping circles).
Pi
A constant, irrational number derived from the ratio of the circumference of a circle to its diameter. Pi always has the same value, regardless of the size of a circle. This value has been calculated to many trillions of digits, but 3.141 is fine for our purposes.


OTHER

Parallelogram
An enclosed two-dimensional shape wherein all opposing sides are parallel.
Polygon
An enclosed two-dimensional shape with a finite number of straight sides.
Quadrilateral
A polygon with exactly four sides.

A TABLE OF GEOMETRIC SYMBOLS

Symbol Name Example Meaning
\Delta Triangle \Delta ABC The triangle with points A, B and C.
\angle Angle \angle A = 23° Angle A is 23 degrees.
\overline{AB} Line Segment \overline{AB} = 2.4 ft The distance between points A and B is 2.4 feet.
\overset{\rightarrow}{AB} Ray \overset{\rightarrow}{AB} The line that begins at point A and continues through point B to infinity.
\overleftrightarrow{AB} Line \overleftrightarrow{AB} The infinite line that passes through or has points A and B.
Therefore a – b = c

∴ c + b = a

a minus b is c, therefore c plus b is equal to a.
< and > Less/Greater Than a < b Length a is smaller than length b.
≤ and ≥ Less/Greater Than Or Equal To a < b ≥ c a is smaller than b, b is larger than or equal to c.
\approx Is Almost Equal To a \approx x The difference between a and x is negligible.
\perp Perpendicular To AB \perp BC Line AB is perpendicular to Line BC.
\infty Infinity \overleftrightarrow{AB} = \infty Line AB has infinite length.
r Radius r = 16.5 The radius is 16.5 units in length
d Diameter d = 50 The diameter is 50 units in length
Circle ⊙A<⊙B Circle named A is smaller than Circle named B.
π Pi (Pronounced ‘pie’) π = C/D Pi equals the circumference of a circle divided by that circles diameter.
\cong Congruent To AB \cong BC Lines AB and BC are of equal length, they are congruent to each other.