Plane Geometry , math
-
Upload
mariejane-orpilla-llanes -
Category
Documents
-
view
248 -
download
0
Transcript of Plane Geometry , math
-
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.