Matemáticas
Quadrilateral: Naming a Four-Sided Shape from Its Properties
A quadrilateral has four straight sides and angles adding to 360°. Compare square, rectangle, rhombus, parallelogram, kite and trapezium side by side.
Quadrilateral
A quadrilateral is a flat shape with four straight sides and four corners, whose interior angles always add up to 360 degrees.
- También llamado
- Four-sided polygon
- Dónde lo encuentra el alumnado
- Grade 4 mathematics, when shapes are first sorted by their properties, and again at GCSE wherever a missing angle in a four-sided figure has to be found.
La respuesta corta
A quadrilateral is any flat, closed shape with four straight sides. Its four interior angles always add up to 360 degrees, because a diagonal splits it into two triangles. The named quadrilaterals — square, rectangle, rhombus, parallelogram, kite, trapezium and isosceles trapezium — are separated by their sides, angles, diagonals and symmetry.
Un ejemplo
85° + 100° + 120° + d = 360°, so d = 55°
Three angles of a quadrilateral are given as 85, 100 and 120 degrees. Those total 305, and since all four must reach 360, the missing angle is 55 degrees. Nothing about the particular shape is needed here — the sum holds for every quadrilateral, so the working is the same whether the figure is a kite, a trapezium or something with no name at all.
Four straight sides, and one consequence
The definition is as plain as it looks: four straight sides, joined end to end, enclosing a region. Nothing is said about the sides being equal or the corners being right angles, which is why a neat square and a lopsided four-sided sketch are the same kind of object.
One fact follows from that definition and is worth more than the definition itself. Draw a diagonal across any quadrilateral and it becomes two triangles. Each triangle's angles add to 180 degrees, so the four angles of the quadrilateral add to 360. That holds for concave shapes as well as convex ones.
Naming a shape when all you are given is its properties
Questions rarely announce that a shape is a rhombus. They hand over three facts — four equal sides, opposite angles equal, diagonals crossing at right angles — and expect the name. The seven quadrilaterals a school syllabus names apart are separated cleanly by sides, angles, diagonals and symmetry.
The arrowhead, sometimes called a delta, is a kite pushed inwards so that one interior angle is bigger than 180 degrees. It keeps the kite's single line of symmetry and is the only one of these shapes that is concave.
- Square — four equal sides, four right angles, equal diagonals that bisect each other at right angles, four lines of symmetry, rotational symmetry of order 4
- Rectangle — opposite sides equal, four right angles, equal diagonals that bisect each other but not at right angles, two lines of symmetry, order 2
- Rhombus — four equal sides, opposite angles equal, diagonals bisecting each other at right angles and bisecting the corner angles, two lines of symmetry, order 2
- Parallelogram — two pairs of parallel equal sides, opposite angles equal, diagonals bisecting each other, no line of symmetry, order 2
- Kite — two pairs of adjacent equal sides, one pair of equal opposite angles, diagonals meeting at right angles with the longer bisecting the shorter, one line of symmetry, order 1
- Trapezium — one pair of parallel sides, no equal sides guaranteed, no line of symmetry, order 1
- Isosceles trapezium — one pair of parallel sides plus equal slant sides, equal base angles, equal diagonals, one line of symmetry, order 1
The categories overlap on purpose
A square is a rectangle. It is also a rhombus, a parallelogram and a kite. That is not a trick question — the names describe properties, and a square happens to hold all of them at once. The reliable habit is to check the shape against each definition rather than against the picture printed in the textbook.
Reading the relationship backwards does not work. Every square is a rhombus, but most rhombuses are not squares, and a question that says "rhombus" has not told you the angles are right angles. Assuming otherwise turns a correct method into a wrong answer.
- The interior angle sum of every quadrilateral, convex or concave
- 360°The interior angle sum of every quadrilateral, convex or concave
Preguntas frecuentes
Is a square a quadrilateral?
Yes. A square has four straight sides, so it satisfies the definition completely. It is also the most specific quadrilateral there is: every property the other named shapes have — equal sides, right angles, equal diagonals, diagonals meeting at right angles — a square has all of them together, which is why it belongs to several categories at once.
What are the seven quadrilaterals?
Square, rectangle, rhombus, parallelogram, kite, trapezium and isosceles trapezium. Some syllabuses add the arrowhead, a concave kite with one reflex angle. Beyond those, a four-sided shape with no special properties is simply a quadrilateral — the name is not a failure to identify it, it is the correct answer.
Do the angles of a quadrilateral always add up to 360 degrees?
Always, including the concave ones with a reflex angle. The reason is the diagonal split: any quadrilateral divides into two triangles, each contributing 180 degrees. This is why three given angles are enough to find the fourth, whatever the shape is called.
What is the difference between a quadrilateral and a polygon?
A polygon is any closed shape made of straight sides. A quadrilateral is the polygon that has exactly four of them, in the same way a triangle is the one with three and a pentagon the one with five. Every quadrilateral is a polygon; most polygons are not quadrilaterals.
Fuentes
- National curriculum in England: mathematics programmes of study — Department for Education
Última actualización
Saber la palabra no es lo mismo que usarla
Un profesor puede ver al alumno usarlo en un ejercicio y detectar justo dónde se detiene la comprensión. La primera clase es gratuita.