Varsity Tutors does not have affiliation with universities mentioned on its website. Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors.Īward-Winning claim based on CBS Local and Houston Press awards. Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC.Ĥ.9/5.0 Satisfaction Rating based upon cumulative historical session ratings through 12/31/20. The following Venn Diagram shows the inclusions and intersections of the various types of quadrilaterals. Venn Diagram of Quadrilateral Classification Quadrilateral is a four-sided polygon that has no congruent sides. Some textbooks say a kite has at least two pairs of adjacent congruent sides, so a rhombus is a special case of a kite.) Is a quadrilateral with exactly two pairs of adjacent congruent sides. Is a trapezoid whose non-parallel sides are congruent. in America, trapezium usually means a quadrilateral with no parallel sides.) (There may be some confusion about this word depending on which country you're in. Is a quadrilateral with exactly one pair of parallel sides. On the other hand, not all quadrilaterals and parallelograms are rectangles.Ī rectangle has all the properties of a parallelogram, plus the following:Ī rhombus has all the properties of a parallelogram, plus the following:Ĭan be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles. Is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. Is a quadrilateral in which both pairs of opposite sides areĪ parallelogram also has the following properties: Here we show four different vertices meeting at point D.There are many special types of quadrilateral. Notice that the four different vertices of the kite always meet at a point. Rotate ABCD 180° around middle point of CD Rotate ABCD 180° around middle point of BC Rotate ABCD 180° around the middle point of AB (Or design your own!) To get your started, we included some pictures. Print out and color several identical kites using the printable page below. The picture at the top of this page is an example. Such rotations fill the whole plane with copies of the kite. In order to cover the plane, you will rotate each kite 180° around the middle point of each of its sides. We will use kites to tessellate the plane. (Some of these tessellations are quite interesting.) Less obvious but true is a more general fact that every kite tessellates the plane. It is easy to see that every rectangle tessellates the plane. So the sum of the angles of a kite is 360 degrees. (Can you prove it?)Įvery kite can be decomposed into two triangles. In addition, in every convex kite, the sum of the diagonals is longer than 1/2 of the perimeter. In convex kites, the diagonals intersect in concave (not convex) kites, they do not.Įvery diagonal is shorter than 1/2 of the perimeter. In figure 4, the diagonals, shown as dotted blue lines, are respectively, In figure 1 there is only one possible kite with these corners. This means that no three of them are on the same straight line.īut four corners do not always determine a kite in a single unique way. In order to form four corners of a kite, four points on the plane must be "independent". Sometimes rhombuses are excluded by the additional condition that not all sides are of equal length.]Ī quadrilateral, also called a kite, is a polygon that has four sides. Sometimes only convex quadrilaterals are called kites and non-convex ones are called arrowheads. These two definitions include rhombuses and non-convex quadrilaterals. This definition is equivalent to the following one: A kite is quadrilateral that has two pairs of equal adjacent sides. The most general definition that is typically used: A kite is a quadrilateral in which one of its diagonals is its axis of symmetry. Usually a kite is described as a special kind of quadrilateral, but the exact definitions often vary. This is not the standard definition of a kite. In this unit we call all quadrilaterals kites.
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