Simple quadrilaterals’ angles always total 360 degrees
A quadrilateral is a four-sided polygon—four edges, four vertices—from Latin quadri and latus, also called a tetragon in Greek style. Figures may be simple or self-intersecting complex; simple ones are convex or concave. Interior angles of a simple planar quadrilateral sum to 360°.
The Latin roots quadri, four, and latus, side, give the usual name, while the Greek-style tetragon and quadrangle count corners instead. In a convex quadrilateral both diagonals run inside the figure. The family tree begins with the trapezoid, which in American usage needs at least one pair of parallel sides and so includes parallelograms, though British English calls it a trapezium. An isosceles trapezoid has equal base angles, or equivalently equal diagonals.
A parallelogram has two pairs of parallel sides, which is the same as saying opposite sides are equal, opposite angles are equal, or the diagonals cut each other in half. A rhombus has four equal sides and perpendicular bisecting diagonals, informally a pushed-over square; a rhomboid is its lopsided cousin with unequal neighbouring sides and no right angles. Rectangles have four right angles and equal diagonals, and a square is exactly a figure that is both a rhombus and a rectangle. An oblong is any rectangle that is not a square.
A kite has two pairs of equal adjacent sides, perpendicular diagonals and one diagonal splitting it into congruent triangles. A convex quadrilateral can hold an inscribed circle exactly when its opposite sides have equal sums, and its corners sit on one circle exactly when opposite angles add to 180 degrees; shapes doing both are bicentric, and a right kite, with two opposite right angles, is one example. Harmonic quadrilaterals are cyclic ones whose opposite sides have equal products.
The more exotic names include the equilic quadrilateral, whose two equal opposite sides meet at 60 degrees when extended, the Watt quadrilateral with one pair of equal opposite sides, and the diametric quadrilateral, a cyclic figure with one side forming a diameter of its circle.
Source: Quadrilateral
