
Plane Figures








Plane Geometry



Introduction
The part of geometry which studies twodimensional figures drawn on a flat surface is known as plane geometry. This knowledge is very important because many problems people attempt to solve in everyday life are either twodimensional by nature, or they can be simplified into two dimensions.
Many problems might appear to be threedimensional at first glance, but they are actually twodimensional. One such example is a stream of water coming out of a stationary garden hose or a fire hose. This is because the water is always on a plane  a vertical plane. The elimination of the third dimension makes it much easier to study the projectile motion.
Although many problems are truly threedimensional, we may simplify them into twodimensional problems to make a solution easier, if we can do that with reasonable accuracy. For example, plane surveys always treat any small segment of land as a horizontal plane.
When observing nature closely, we find that the seemingly unusual and complicated shapes are merely extensions of a few simple basic figures. In plane geometry, these simple basic shapes include point, line, triangle, quadrilateral, manysided polygons, and circle. Each has a distinct character of its own. When combined to form a unique object, new properties and useful applications are formed.







Triangles

A triangle is a closed plane geometric figure formed by connecting the endpoints of three line segments
endpoint to endpoint.






Quadrilaterals

A quadrilateral is a foursided closed plane figure.






Parallelograms

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.






Rectangles

A rectangle is a quadrilateral that has four right angles.






Rhombi

When a quadrilateral has four congruent sides, it is called a rhombus. A rhombus is actually an equilateral
parallelogram.






Squares

A square is a quadrilateral with four congruent sides and four right angles.






Trapezoids

If a quadrilateral has only one pair of opposite sides that are parallel, then the quadrilateral is a trapezoid.
The parallel sides are called bases. The nonparallel sides are called legs.






Polygons

Since poly means many and gon means angles, polygon means many angles. In geometry, a polygon is a
closed plane figure formed by three or more line segments called sides. Each side intersects exactly two
other sides, one at each endpoint. No two sides with a common endpoint are collinear.






Circles

A circle is the set of points on a plane that are equidistant from a fixed point known as the center. A circle
is named by its center.



