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...)
(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.
Remember about quadrilaterals:
Parallelogram: it is a quadrilateral in which opposite sides are parallel.
Rectangle: a parallelogram in which opposite sides are equal and each of
whose angle is
90
Square: it is a rectangle having all sides equal.
Rhombus: is a parallelogram having all sides equal.
Trapezoid: it is a quadrilateral in which two opposite sides are parallel
and other two opposite sides are non parallel.
Kite: it is a quadrilateral in which two pairs of adjacent sides are equal.
The video above will explain more in detail about Quadrilateral types and their relationship, with the help of several examples.
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