What does diagonal mean?
A diagonal is a straight line that connects two non-adjacent corners, or vertices, of a shape such as a square, rectangle, or cube. Unlike a side, which runs along the boundary of a figure, a diagonal cuts across its interior. The word also functions as an adjective meaning slanting or oblique: a diagonal stripe, for instance, runs at an angle rather than horizontally or vertically. Beyond geometry, the term appears in everyday contexts — fabric may be cut on the diagonal, a photographer may compose along diagonal lines to create a sense of movement, and in chess a bishop travels along diagonals of the board. Derived from the Greek diagonios, meaning "from angle to angle," the word entered English through Latin in the sixteenth century. It carries no emotional connotation and is equally at home in formal mathematical prose and casual conversation, making it a precise yet versatile term for describing anything that runs at a slant.
A straight line segment joining two non-adjacent vertices of a polygon or polyhedron.
"Draw both diagonals of the rectangle and mark where they intersect."
In strict geometric usage, applies only to polygons (two dimensions) and polyhedra (three dimensions); extended loosely to grids, matrices, and game boards.
(in board games) A slanted line of squares across a playing board.
"Her bishop controlled the entire long diagonal."
Common in chess and draughts commentary.
Slanting; lying on, following, or extending in a direction between horizontal and vertical.
"The jacket featured bold diagonal stripes across the chest."
Often used attributively before a noun (diagonal line, diagonal cut).
Standard plural; used when referring to multiple such lines, e.g. the two diagonals of a quadrilateral.
"The two diagonals of a rhombus are perpendicular to each other."
Every square has exactly two diagonals that cross at a perfect 90° angle and bisect each other — a fact ancient Greek geometers found so elegant they built whole proofs around it.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of diagonal
Diagonal derives from the Greek diagonios, formed from dia- ("across, through") and gonia ("angle"), so literally "from angle to angle." Latin adopted the term as diagonalis, and English acquired it via French or directly from Latin around the mid-sixteenth century. It shares the root gonia with words such as "polygon," "pentagon," and "trigonometry." The related verb "diagonalize" and the adverb "diagonally" developed later as natural derivatives within English.
Related word forms
How diagonal is actually used
"Diagonal" is neutral in register and common in both everyday speech and technical writing in mathematics, geometry, design, textiles, photography, and games. In geometry it is used precisely for lines between non-adjacent vertices; more loosely, it simply means "slanting." The phrase "on the diagonal" (or "at a diagonal") is idiomatic in cooking, sewing, and art direction to mean cutting or arranging at an angle rather than parallel to the edges.
Easily confused with diagonal
A cathetus is one of the sides forming a right angle in a right triangle, whereas a diagonal joins non-adjacent vertices of a polygon.
The hypotenuse is specifically the side opposite the right angle in a right triangle; a diagonal is any line connecting two non-adjacent vertices of a polygon or polyhedron.