Right angle

Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to vectors.

The meaning of right in right angle possibly refers to the Latin adjective rectus 'erect, straight, upright, perpendicular'.

It should not be confused with the similarly shaped symbol U+231E ⌞ BOTTOM LEFT CORNER (⌞, ⌞).

The symbol for a measured angle, an arc, with a dot, is used in some European countries, including German-speaking countries and Poland, as an alternative symbol for a right angle.

One may argue that, even if postulate 4 can be proven from the preceding ones, in the order that Euclid presents his material it is necessary to include it since without it postulate 5, which uses the right angle as a unit of measure, makes no sense.

From the angle in question, running a straight line along one side exactly three units in length, and along the second side exactly four units in length, will create a hypotenuse (the longer line opposite the right angle that connects the two measured endpoints) of exactly five units in length.

Two application examples in which the right angle and the Thales' theorem are included (see animations).