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a quadrilateral with 4 congruent sides

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From Wikipedia


In Euclidean plane geometry, a quadrilateral is a polygon with four sides (or 'edges') and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The word quadrilateral is made of the words quad (meaning "four") and lateral (meaning "of sides").

Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting), also called crossed. Simple quadrilaterals are either convex or concave.

The interior angles of a simple quadrilateral add up to 360 degrees of arc. In a crossed quadrilateral, the interior angles on either side of the crossing add up to 720°.

All convex quadrilaterals tile the plane by repeated rotation around the midpoints of their edges.

Convex quadrilaterals - parallelograms

A parallelogram is a quadrilateral with two pairs of parallel sides. Equivalent conditions are that opposite sides are of equal length; that opposite angles are equal; or that the diagonals bisect each other. Parallelograms also include the square, rectangle, rhombus and rhomboid.

  • Rhombus or rhomb: all four sides are of equal length. Equivalent conditions are that opposite sides are parallel and opposite angles are equal, or that the diagonals perpendicularly bisect each other. An informal description is "a pushed-over square" (including a square).
  • Rhomboid: a parallelogram in which adjacent sides are of unequal lengths and angles are oblique (not right angles). Informally: "a pushed-over rectangle with no right angles."
  • Rectangle: all four angles are right angles. An equivalent condition is that the diagonals bisect each other and are equal in length. Informally: "a box or oblong" (including a square).
  • Square (regular quadrilateral): all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), that the diagonals perpendicularly bisect each other, and are of equal length. A quadrilateral is a square if and only if it is both a rhombus and a rectangle.
  • Oblong: a term sometimes used to denote a rectangle which has unequal adjacent sides (i.e. a rectangle that is not a square).

A shape that is both a rhombus (four equal sides) and a rectangle (four equal angles) is a square (four equal sides and four equal angles).

Convex quadrilaterals - other

  • Kite: two pairs of adjacent sides are of equal length. This implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. It also implies that the diagonals are perpendicular. (It is common, especially in the discussions on plane tessellations, to refer to the concave quadrilateral with these properties as a dart or arrowhead, with term kite being restricted to the convex shape.)
  • Orthodiagonal quadrilateral: the diagonals cross at right angles.
  • Trapezium (British English) or trapezoid (NAm.): one pair of opposite sides are parallel.
  • Isosceles trapezium (Brit.) or isosceles trapezoid (NAm.): one pair of opposite sides are parallel and the base angles are equal in measure. This implies that the other two sides are of equal length, and that the diagonals are of equal length. An alternative definition is: "a quadrilateral with an axis of symmetry bisecting one pair of opposite sides".
  • Trapezium (NAm.): no sides are parallel. (In British English this would be called an irregular quadrilateral, and was once called a trapezoid.)
  • Cyclic quadrilateral: the four vertices lie on a circumscribed circle. A quadrilateral is cyclic if and only if opposite angles sum to 180°.
  • Tangential quadrilateral: the four edges are tangential to an inscribed circle. Another term for a tangential polygon is inscriptible.
  • Bicentric quadrilateral: both cyclic and tangential.

Area of a convex quadrilateral

There are various general formulas for the area of a convex quadrilateral.

The area of a quadrilateral ABCD can be calculated using vectors. Let vectors AC and BD form the diagonals from A to C and from B to D. The area of the quadrilateral is then

\frac{1}{2} |{AC}\times{BD}|,

which is the magnitude of the cross product of vectors AC and BD. In two-dimensional Euclidean space, expressing vector AC as a free vector in Cartesian space equal to (x1,y1) and BD as (x2,y2), this can be rewritten as:

From Yahoo Answers

Question:a shape

Answers:a rectangle

Question:what is: A quadrilateral with 4 congruent angles called: What is a : quadrilateral with 4 congruent sides called: PLEASE HELP!

Answers:4 congruent angles: each angle is 90 so that would be a RECTANGLE 4 congruent sides: RHOMBUS


Answers:Take a rectangle.

Question:If a quadrilateral has 4 congruent sides, but its diagnols are not congruent, then the quadrilateral is a ...??? (diagonal- lines drawn from 1 vertex 2 another.) Which description of a parallelogram is incorrect?? a) quadrilateral with 2 pairs of parallel opposite sides b) quadrilateral with opposite sides congruent c) 4-sided polygon with opposite sides parallel d) polygon with opposite sides parallel

Answers:First question: RHOMBUS. A rhombus has four congruent sides, but all four angles are not congruent (although opposite angles are). Since the angles are not all congruent, the diagonals are not congruent. Second question: D. A parallelogram has 4 sides. It does not describe any polygon.

From Youtube

Quadrilateral Rap :A rap to teach you about quadrilaterals. QUADRILATERAL RAP LYRICS Quadrilateral is a four sided polygon Let's draw some up so pick up yo crayons We got one side, two sides, three sides, four Let's start out with a square and then well talk more More, more Talk more More, more All squares have four All the angles are congruent so there known as equal angular You might even hear a square referred to as rectangular Now we got that covered we can move on to the kite Theres so much to say bout this shape we could be here till the night To the night, night To the night To the night, night Yo my name is Black Knight A kite has two pairs of adjacent and congruent sides If anybody disagrees you tell them they just lied Every convex kite seems to have an inscribed circle And if you dont believe me, man you crazy like Steve Urkle Urkle, Urkle Steve Urkle Urkle, Urkle Inscribed circle A trapezoid is the next shape on our list If you don't listen yo your gunna get dissed They got one pair of opposite parallel sides The other two are legs which will always collide Lide, lide Collide Lide, lide Got rules to abide Diagonals in a parallelogram bisect each other If you dont believe me go ahead and ask yo mother Pairs of opposite angles are also congruent If you listen to these properties youll know it fluent Fluent, fluent Fluent, fluent Opposite angles are also congruent Yo look at the time; Ive reached the end of my rap Thank you, thank you no need to clap See you all later hope you have ...