Introduction to Geometry
The Geometry is a category of mathematics concerned with questions of size, shape, figures relative location and the properties of space. The mathematician who works in geometry field is known as a geometer. The Geometry stands separately in a number of early cultures as a body of practical knowledge that is concerning lengths, areas, and volumes with the elements of a formal mathematical science emerging in the West as rapidly as Thales. By the 3rd century BC geometry was put into an axiomatic form through Euclid, whose treatment; Euclidean geometryset a standard for many centuries to follow. The Archimedes developed ingenious techniques for computing volumes and areas, in numerous ways anticipating modern integral calculus. The category of astronomy particularly mapping the positions of the stars and planets on the celestial sphere and explaining the relationship between movements of celestial bodies, served as a major source of geometric problems during the next one and a half millennia. Both the astronomy and geometry were considered in traditional world to be part of the Quadrivium a subset of the seven liberal arts considered necessary for a free citizen to master.
Symbols Used in Geometry
Symbol
Meaning
Example
In Words
Δ
Triangle
ΔABC has 3 equal sides
Triangle ABC has three equal sides
Angle
ABC is 45°
The angle formed by ABC is 45 degrees.

Perpendicular
ABCD
The line AB is perpendicular to line CD
¦
Parallel
EF¦GH
The line EF is parallel to line GH
°
Degrees
360° makes a full circle
Right Angle (90°)
is 90°
A right angle is 90 degrees
Line Segment "AB"
AB
The line between A and B
Line "AB"
The infinite line that includes A and B
Ray "AB"
The line that starts at A, goes through B and continues on
Congruent (same shape and size)
ΔABCΔDEF
Triangle ABC is congruent to triangle DEF
~
Similar (same shape, different size)
ΔDEF~ΔMNO
Triangle DEF is similar to triangle MNO
Therefore
a=bb=a
a equals b, therefore b equals a
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