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. |