Subject: Geometry

# Words & Symbols In Geometry

## Geometry.WordsAndSymbols History

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(:cellnr:) \begin{matrix}\rightarrow\\ AB \end{matrix}

(:cellnr:) \overset{\rightarrow}{AB}

(:cell:) \begin{matrix}\rightarrow\\ AB \end{matrix}

(:cell:) \overset{\rightarrow}{AB}

(:cell:)\overrightarrow{AB} = \infty

(:cell:) \overleftrightarrow{AB} = \infty

(:cellnr:) \overrightarrow{ab}

(:cellnr:) \begin{matrix}\rightarrow\\ AB \end{matrix}

(:cell:) \overrightarrow{ab}

(:cell:) \begin{matrix}\rightarrow\\ AB \end{matrix}

(:cell:)a – b = c ∴ c + b = a

(:cell:)a – b = c

∴ c + b = a

(:cellnr:)≈

(:cellnr:) \approx

(:cell:)a ≈ x

(:cell:) a \approx x

(:table border=1 cellpadding=5 cellspacing=0:)
(:cellnr align=center bgcolor=#d4d7ba:)**Symbol**
(:cell align=center bgcolor=#d4d7ba:)**Name**
(:cell align=center bgcolor=#d4d7ba:)**Example**
(:cell align=center bgcolor=#d4d7ba:)**Meaning**
(:cellnr:) \Delta
(:cell:)Triangle
(:cell:) \Delta ABC
(:cell:)The triangle with points A, B and C.
(:cellnr:) \angle
(:cell:)Angle
(:cell:) \angle A = 23°
(:cell:)Angle A is 23 degrees.
(:cellnr:) \overline{AB}
(:cell:)Line Segment
(:cell:) \overline{AB} = 2.4 ft
(:cell:)The distance between points A and B is 2.4 feet.
(:cellnr:) \overrightarrow{ab}
(:cell:)Ray
(:cell:) \overrightarrow{ab}
(:cell:)The line that begins at point A and continues through point B to infinity.
(:cellnr:) \overleftrightarrow{AB}
(:cell:)Line
(:cell:) \overleftrightarrow{AB}
(:cell:)The infinite line that passes through or has points A and B.
(:cellnr:)∴
(:cell:)Therefore
(:cell:)a – b = c ∴ c + b = a
(:cell:)a minus b is c, therefore c plus b is equal to a.
(:cellnr:)< and >
(:cell:)Less/Greater Than
(:cell:)a < b
(:cell:)Length a is smaller than length b.
(:cellnr:)≤ and ≥
(:cell:)Less/Greater Than Or Equal To
(:cell:)a < b ≥ c
(:cell:)a is smaller than b, b is larger than or equal to c.
(:cellnr:)≈
(:cell:)Is Almost Equal To
(:cell:)a ≈ x
(:cell:)The difference between a and x is negligible.
(:cellnr:) \perp
(:cell:)Perpendicular To
(:cell:) AB \perp BC
(:cell:)Line AB is perpendicular to Line BC.
(:cellnr:) \infty
(:cell:)Infinity
(:cell:)\overrightarrow{AB} = \infty
(:cell:)Line AB has infinite length.
(:cellnr:)r
(:cell:)Radius
(:cell:)r = 16.5
(:cell:)The radius is 16.5 units in length
(:cellnr:)d
(:cell:)Diameter
(:cell:)d = 50
(:cell:)The diameter is 50 units in length
(:cellnr:)⊙
(:cell:)Circle
(:cell:)⊙A<⊙B
(:cell:)Circle named A is smaller than Circle named B.
(:cellnr:)π
(:cell:)Pi (Pronounced ‘pie’)
(:cell:)π = C/D
(:cell:)Pi equals the circumference of a circle divided by that circles diameter.
(:cellnr:) \cong
(:cell:)Congruent To
(:cell:) AB \cong BC
(:cell:)Lines AB and BC are of equal length, they are congruent to each other.
(:tableend:)

(:title 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!)*

(:table border=1 cellpadding=5 cellspacing=0:)
(:cellnr bgcolor=#d4d7ba colspan=14 align=center:) **The Breakdown**
(:cellnr:)

- Definitions for Points, Lines & Planes
- Definitions for Angles
- Definitions for Circles
- Definitions for Other Geometric Words
- Geometric Symbols

(:tableend:)

## 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.