This is a free lesson from our course in Geometry This lesson explains the basics and concepts about the quadrilaterals. You�ll learn it starting from your earlier learning about polygons. All this you�ll learn in the contents presented by the instructor in own handwriting, using video and with the help of several examples with solution. Quadrilateral: in geometry, a plane closed figure formed by four line segments is called a quadrilateral. It is a polygon with four sides, four vertices and with four angles. The interior angles of a quadrilateral add up to 360 . Quadrilaterals are simple i.e. not self-intersecting or complex i.e. self-intersecting. Simple quadrilaterals may be either convex or concave. (More text below video...)
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(Continued from above) There are three topological types of quadrilaterals: convex quadrilaterals, concave quadrilaterals, and crossed quadrilaterals or butterflies type (shown in the figure below): Now you�ll explore more on conceptual understanding about important quadrilaterals (Figure below). Parallelogram- is a quadrilateral with two pairs of parallel sides. Equivalent conditions are that opposite sides are of equal length; the opposite angles are equal and the diagonals bisect each other. Notice: parallelograms also include the rectangle, square, rhombus and rhomboid.
Square: is a regular quadrilateral having all four sides of equal length, and all four angles are right angles. An equivalent condition is that opposite sides are parallel; diagonals are of equal length and bisect each other at right angles. A quadrilateral is a square �if and only� if it is a rhombus and a rectangle both.
Rectangle- is a quadrilateral in which all the four angles are right angles. An equivalent condition is that the diagonals bisect each other and are equal in length.
Trapezoid: is a quadrilateral that has exactly two sides parallel, but it's a type of quadrilateral that is not a parallelogram. One of the parallel sides is the base and the non-parallel sides are legs.
Rhombus: is a quadrilateral in which all the four sides are of equal length. Equivalent conditions are that opposite sides are parallel and opposite angles are equal. The diagonals perpendicularly bisect each other.
Kite: is a quadrilateral in which two adjacent sides are of equal length and the other two sides are also equal. Thus the angles between the two pairs of equal sides are equal, and the diagonals are perpendicular.
Furthermore, you�ll learn the relationship with the help of the �Venn Diagram� i.e. the position and overlap of the circles indicating the relationships between the quadrilaterals and that helps you better understand to put together various types of quadrilaterals: Notice in the figure above, how different quadrilaterals relate to each other i.e. the relationship amongst important quadrilateral group types i.e. trapezoids, parallelograms and general quadrilaterals.
Rectangle: a parallelogram in which opposite sides are equal and each of whose angle is 90 