8/13/2019 Plane Geometry , math

1/8

Plane GeometryIntroduction

The part

of

geometry which

studies

two-dimensio

nal

figures

drawn ona flat

surfaceis knownas plane

geometr

y. This

knowledge is

very

important because

many

problemspeopleattempt

to solve

ineveryday

life are

eithertwo-

dimensio

nal by

nature,or they

can be

simplified into

two

dimensio

geometry

plane geometry

three-dimensional

two-dimensional

2-Dimensional

Common Plane

Figures

Topic Assessment

http://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/g/geometry.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/g/geometry.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/p/planegeometry.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/p/planegeometry.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/t/three-dimensional.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/t/three-dimensional.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/t/two-dimensional.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/t/two-dimensional.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/d2in3d/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/d2in3d/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/geo-common-figures-in-plane.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/geo-common-figures-in-plane.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/geo-common-figures-in-plane.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/assessment/planefigures.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/assessment/planefigures.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/assessment/planefigures.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/geo-common-figures-in-plane.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/geo-common-figures-in-plane.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/d2in3d/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/t/two-dimensional.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/t/three-dimensional.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/p/planegeometry.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/vmd/full/g/geometry.htm

8/13/2019 Plane Geometry , math

2/8

ns.

Many

problemsmight

appear tobe three-dimensio

nal at

first

glance,but they

are

actually

two-dimensio

nal. Onesuchexample

is a

stream ofwater

coming

out of astationar

y garden

hose or a

fire hose.This is

because

the water

is alwayson a

plane - a

verticalplane.

The

eliminati

on of thethird

dimensio

n makesit much

easier tostudy the

projectil

8/13/2019 Plane Geometry , math

3/8

emotion.

Although many

problemsare trulythree-

dimensio

nal, we

maysimplify

them

into two-

dimensional

problemsto makea

solution

easier, ifwe can

do that

withreasonab

le

accuracy

. Forexample,

plane

surveys

alwaystreat any

small

segmentof land

as a

horizont

al plane.

When

observing nature

closely,

we findthat the

8/13/2019 Plane Geometry , math

4/8

8/13/2019 Plane Geometry , math

5/8

applications are

formed.

Triangles

A triangle is a closed plane geometricfigure formed by connecting the endpoints

of three line segments endpoint to

endpoint.

Animation

Triangle VR

Sum of InteriorAngles

Three Sides

Sum of Interior

Angles

Quadrilaterals

A quadrilateral is a four-sided closed plane

figure.Animation

Parallelograms

A parallelogram is a quadrilateral withboth pairs of opposite sides parallel.

Animation #1

Animation #2

Parallelogram VR

http://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/triangle.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/triangle.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/bike/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/bike/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/sum-angle-measures.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/sum-angle-measures.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/sum-angle-measures.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/triangles-1.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/triangles-1.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/triangles-2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/triangles-2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/triangles-2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/quadrila.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/quadrila.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/paragram.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/paragram.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/paragra2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/paragra2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/paragram/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/paragram/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/paragram/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/paragra2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/paragram.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/quadrila.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/triangles-2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/triangles-2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/exercises/demop/triangles-1.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/sum-angle-measures.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/sum-angle-measures.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/bike/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/triangle.htm

8/13/2019 Plane Geometry , math

6/8

ParallelogramManipulation

Rectangles

A rectangle is a quadrilateral that has fourright angles.

AnimationRectangle

Manipulation

Rhombi

When a quadrilateral has four congruent

sides, it is called a rhombus. A rhombus isactually an equilateral parallelogram. Animation #1

Animation #2

Animation #3

RhombusManipulation

http://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-para.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-para.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-para.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rectangl.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rectangl.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rect.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rect.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rect.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombus.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombus.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombus2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombus2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombu3.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombu3.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rhombus.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rhombus.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rhombus.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rhombus.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rhombus.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombu3.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombus2.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rhombus.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rect.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-rect.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/rectangl.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-para.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-para.htm

8/13/2019 Plane Geometry , math

7/8

Squares

A square is a quadrilateral with four

congruent sides and four right angles.Animation

SquareManipulation

Trapezoids

If a quadrilateral has only one pair ofopposite sides that are parallel, then the

quadrilateral is a trapezoid. The parallelsides are called bases. The non-parallel

sides are called legs.

Animation

TrapezoidManipulation

Polygons

Since poly means many and gon meansangles, polygon means many angles. In

geometry, a polygon is a closed planefigure formed by three or more line

segments called sides. Each side intersects

exactly two other sides, one at each

Animation

Polygon VR

http://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/square.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/square.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-square.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-square.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-square.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/trapezoi.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/trapezoi.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-trape.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-trape.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-trape.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/polygons.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/polygons.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/polygons/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/polygons/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/vr/polygons/index.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/polygons.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-trape.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-trape.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/trapezoi.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-square.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/exp/prop-square.htmhttp://images.schoolinsites.com/websites/nyecounty/nyecounty/mines/mines68/media/ani/square.htm

8/13/2019 Plane Geometry , math

8/8

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.