Three-line octagon refers to the eight angles formed by two straight lines being intercepted by a straight line. The first and second straight lines are called intercepted lines, and the third straight line is called the intercepting line. Isotopic angles, interior angles, etc. appear in pairs. We cannot say "∠5 is an interior angle", "∠6 is an interior angle on the same side", etc.

Properties of Three Lines and Octagons

The eight angles have different names according to their relative positions, as shown in the figure below.

Isotropic angles: ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8 have the same relative position, which is called "isotropic angle" . The isotopic angle is shaped like the letter F. If two transverse lines are parallel, the number of angles in the same position is equal.

Staggered angles in the same direction: ∠1 and ∠8, ∠4 and ∠5, ∠3 and ∠6, ∠2 and ∠7 are in the same direction of the intercepted line, but are staggered by the intercepted line, which is called "Same direction and wrong angle". (It can only be used with theoretical verification)

Internal staggered angles: ∠2 and ∠8, ∠3 and ∠5 are intertwined with each other, and they are all inside, called "internal staggered angles". The shape of the internal offset angle is like the letter Z.

External offset angles: ∠1 and ∠7, ∠4 and ∠6 intersect with each other, and are all on the outside, called "external offset angles". (It can only be used with theoretical verification)

Interior angles on the same side: ∠2 and ∠5, ∠3 and ∠8 are on the same side of the section line, and they are all inside, which are called "interior angles on the same side". The inner corner on the same side is shaped like the letter U or a door frame.

Exterior angles on the same side: ∠1 and ∠6, ∠4 and ∠7 are on the same side of the transect, and they are all outside, which are called "external angles on the same side". The shape of the same exterior angle resembles the Greek letter π.