Editing Euclidean geometry (section)

==Notation and terminology==

===Naming of points and figures===
Points are customarily named using capital letters of the alphabet. Other figures, such as lines, triangles, or circles, are named by listing a sufficient number of points to pick them out unambiguously from the relevant figure, e.g., triangle ABC would typically be a triangle with vertices at points A, B, and C.

=== Complementary and supplementary angles ===
Angles whose sum is a right angle are called [[Complementary angles|complementary]]. Complementary angles are formed when a ray shares the same vertex and is pointed in a direction that is in between the two original rays that form the right angle. The number of rays in between the two original rays is infinite.

Angles whose sum is a straight angle are [[Supplementary angles|supplementary]]. Supplementary angles are formed when a ray shares the same vertex and is pointed in a direction that is in between the two original rays that form the straight angle (180 degree angle). The number of rays in between the two original rays is infinite.

=== Modern versions of Euclid's notation ===
In modern terminology, angles would normally be measured in [[degree (angle)|degree]]s or [[radian]]s.

Modern school textbooks often define separate figures called [[line (geometry)|line]]s (infinite), [[Line (mathematics)#Ray|rays]] (semi-infinite), and [[line segment]]s (of finite length). Euclid, rather than discussing a ray as an object that extends to infinity in one direction, would normally use locutions such as "if the line is extended to a sufficient length", although he occasionally referred to "infinite lines". A "line" for Euclid could be either straight or curved, and he used the more specific term "straight line" when necessary.