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Quadrilaterals are four-sided polygons integral to geometry, with types like squares, rectangles, and kites. Each has unique properties, such as side lengths and angles, which determine formulas for calculating their perimeter and area. Understanding these properties is crucial for solving geometric problems involving these shapes.
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Quadrilaterals are polygons with four sides, four vertices, and four angles
Latin roots
The name "quadrilateral" comes from the Latin words for "four" and "sides."
Other names
Quadrilaterals are also known as tetragons or quadrangles
The sum of interior angles is always 360 degrees, and there are two diagonals that connect non-adjacent vertices
Squares have four equal sides, four right angles, and perpendicular diagonals that bisect each other
Rectangles have equal opposite sides, four right angles, and congruent diagonals that bisect each other
Parallelograms have equal opposite sides and angles, with diagonals that bisect each other but are not necessarily equal
Trapezoids have one pair of parallel sides and may have non-parallel sides of different lengths
Rhombuses have four equal sides and perpendicular diagonals that bisect each other, but their angles are not necessarily right angles
Kites have two distinct pairs of adjacent equal sides and diagonals that intersect at a right angle
Quadrilaterals are typically named based on the sequence of their vertices, with labels assigned alphabetically
Sides and vertices
Quadrilaterals can be measured by calculating the lengths of their sides and diagonals, as well as identifying their vertices
Interior angles
The sum of interior angles is always 360 degrees, and adjacent angles may be supplementary or complementary
Perimeter
The perimeter of a quadrilateral is the sum of its side lengths
Area
The area of a quadrilateral varies depending on its type, with formulas for squares, rectangles, parallelograms, trapezoids, rhombuses, and kites
Vertically opposite angles
Vertically opposite angles are congruent
Corresponding angles
Corresponding angles formed by a transversal and two parallel lines are congruent
Exterior angles
The exterior angles of a quadrilateral have a sum of 360 degrees
A deep understanding of quadrilateral properties and formulas is essential for accurately solving geometric problems
00
A key characteristic of a ______ is that the total of its interior angles always adds up to ______ degrees.
quadrilateral
360
01
Square properties
Equilateral, equiangular, perpendicular bisecting diagonals.
02
Rectangle distinctives
Equal opposite sides, four right angles, congruent bisecting diagonals.
