![]() The kites are the quadrilaterals that have an axis of symmetry along one of their diagonals. Exactly one pair of opposite angles are bisected by a diagonal.One diagonal is a line of symmetry (it divides the quadrilateral into two congruent triangles).(In the concave case it is the extension of one of the diagonals.) One diagonal is the perpendicular bisector of the other diagonal.Two pairs of adjacent sides are equal (by definition).CharacterizationsĪ quadrilateral is a kite if and only if any one of the following statements is true: The tiling that it produces by its reflections is the deltoidal trihexagonal tiling. There are only eight polygons that can tile the plane in such a way that reflecting any tile across any one of its edges produces another tile one of them is a right kite, with 60°, 90°, and 120° angles. That is, for these kites the two equal angles on opposite sides of the symmetry axis are each 90 degrees. the kites that can be inscribed in a circle) are exactly the ones formed from two congruent right triangles. The kites that are also cyclic quadrilaterals (i.e. Real-life Application with SolutionĪ park is shaped like a kite with 100 meters and 60 meters diagonals.An equidiagonal kite that maximizes the ratio of perimeter to diameter, inscribed in a Reuleaux triangleĪmong all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite with angles π/3, 5π/12, 5π/6, 5π/12. Hence, the perimeter of the kite is 16 ft. A kite has two pairs of adjacent equal sides, then the length of the fourth side is 5 ft. The lengths of a kite’s three sides are three ft., 5 ft, and 3 ft.Ī. Therefore, the area of the kite is 48 cm 2. Given a kite with diagonals 8 cm and 12 cm, calculate its area. The diagonals of a kite are always equal in length.įalse a kite’s two diagonals are not the same length. Therefore, the area of the kite is 16 square units. The figure below represents a kite.Ī kite’s area is equal to half of the product of its diagonals. The vertices where the congruent sides meet are called the non-adjacent or opposite vertices. DefinitionĪ kite is a type of quadrilateral having two pairs of consecutive, non-overlapping sides that are congruent (equal in length). The concept of kites aligns with the following Common Core Standards:Ĥ.G.A.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size.ĥ.G.B.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.Ħ.G.A.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing them into rectangles or decomposing them into triangles and other shapes. Kites belong to the domain of Geometry, specifically the subdomain of Quadrilaterals, which deals with studying different types of four-sided polygons. However, the complexity of problems involving kites can vary, making them relevant for students in higher grades. Kites are generally introduced to students around 4th to 6th grade as they start learning about different quadrilateral shapes and their properties. We will cover grade appropriateness, math domain, common core standards, definition, key concepts, illustrative examples, real-life applications, practice tests, and FAQs related to kites. This article is designed to give students an in-depth understanding of kites, their properties, and how they can be applied to real-life situations. ![]()
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