Geometric figures

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  • Предмет:
    Математика
  • Язык:
    Английский
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  • Опубликовано:
    2013-12-10
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Geometric figures

Armenian state pedagogical university after khachatur abovyan

Faculty of Mathematics, Physics and Informatics










: Geometric figures



Piruza MkhitaryanSupervisor:. Baghdasaryan




2013

of content

Introduction

1. Polygons

.   Triangles

.   Quadrilateral

.   Circlesonclusion

References

Glossary

Introduction

Geometry is a branch of mathematics <#"700677.files/image001.gif">

A polygon with  vertices (and  sides) is known as an -gon. A polygon for which the only points of the plane belonging to two polygon edges of are the polygon vertices is said to be a simple polygon <#"700677.files/image002.jpg"> sides. The words for polygons with  sides (e.g., pentagon <#"700677.files/image002.jpg">-gon" explicitly. For some polygons, several different terms are used interchangeably, e.g., nonagon and enneagon both refer to the polygon with  sides.

. Triangles

A triangle is a 3-sided polygon <#"700677.files/image005.gif">

polygon

n

2

digon <#"700677.files/image006.gif">

is common to label the vertices of a triangle in counterclockwise order as either  , (or). The vertex angles <#"700677.files/image009.jpg"> (or) are also sometimes used, but this convention results in unnecessary confusion with the common notation for trilinear coordinates <#"700677.files/image011.gif">, and so is not recommended. The sides opposite the angles(are then labeled  with these symbols also indicating the lengths of the sides.are different types of triangles.

Triangles can be classified according to the relative lengths of their sides:

·              In an equilateral triangle <#"700677.files/image015.gif"> <#"700677.files/image016.gif"> <#"700677.files/image017.gif"> <#"700677.files/image018.jpg"> natural numbers  numbers are sides of right triangle.

· Triangles that do not have an angle that measures 90° are called oblique triangles.

·              A triangle that has all interior angles measuring less than 90° is an acute triangle or acute-angled triangle.

·              A triangle that has one interior angle that measures more than 90° is an obtuse triangle or obtuse-angled triangle.

A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral.

 <#"700677.files/image021.gif"> <#"700677.files/image022.gif"> <#"700677.files/image023.gif">

In addition to this there are many types of convex quadrilaterals, such as a parallelogram, rectangle, rhombus, square, trapezoid <#"700677.files/image024.jpg">

A rectangle <#"700677.files/image025.jpg">

rhombus <#"700677.files/image026.jpg">

A square <#"700677.files/image027.gif">

A trapezoid <#"700677.files/image028.gif">

kite has two pairs of sides. Each pair is made up of adjacent sides that are equal in length. The angles are equal where the pairs meet. Diagonals (dashed lines) meet at a right angle, and one of the diagonal bisects (cuts equally in half) the other.

4. Circles

circle is a simple shape <#"700677.files/image030.jpg"> from the center <#"700677.files/image031.jpg"> is called the center <#"700677.files/image032.jpg">. The angle a circle subtends from its center is a full angle <#"700677.files/image033.jpg"> or  radians <#"700677.files/image035.gif">

are two main "slices" of a circle"pizza" slice is called a sector <#"700677.files/image036.jpg">

this paper I have tried to introduce several two-dimensional geometric figures and some of their properties. I introduced triangles, quadrilaterals, polygons, their classifying by different bases, circle and its parts, which are used for solving practical problems.school the course of geometry consist of two parts - plan geometry and space geometry. In school courses plane geometry or two-dimensional geometric figures are studied in 7th, 8th and 9th grade and they are the basis of geometry. Space geometry or three-dimensional geometric shapes are studied in 10th, 11th and 12th grade, but during the study of three-dimensional geometric shapes two-dimensional geometric figures are widely used. In addition to this two-dimensional geometric figures are defined as parts of three-dimensional and n-dimensional shapes. Our world is three- dimensional, that's why we must know common properties of three-dimensional geometric shapes, therefore we must recognize also two-dimensional geometric figures.dimensional geometric figures are widely used in the practise, so everybody must know some properties of geometric figures and their applications.geometry is very beautiful and practice subject and it develops the student’s analytical and visual thinking, which explains its essential role in our life.

Glossary

1.       Point- points are zero-dimensional <#"700677.files/image002.jpg">-gon- A polygon with  vertices and  sides is known as an -gon

7.       Convex <http://mathworld.wolfram.com/ConvexPolygon.html> polygon-A planar polygon <http://mathworld.wolfram.com/Polygon.html> is convex if it contains all the line segments <http://mathworld.wolfram.com/LineSegment.html> connecting any pair of its points

8.       Concave <http://mathworld.wolfram.com/ConcavePolygon.html> polygon-A concave polygon is a polygon <http://mathworld.wolfram.com/Polygon.html> that is not convex <http://mathworld.wolfram.com/ConvexPolygon.html>

.        Triangle- A triangle is a 3-sided polygon <http://mathworld.wolfram.com/Polygon.html> sometimes called the trigon

10.     Triangle geometry <http://mathworld.wolfram.com/TriangleGeometry.html>- The study of triangles is sometimes known as triangle geometry <http://mathworld.wolfram.com/TriangleGeometry.html>

11.     Equilateral triangle <http://en.wikipedia.org/wiki/Equilateral_triangle> - The triangle where all sides have the same length

.        Isosceles triangle-the triangle where two sides are equal in length

.        Scalene triangle- the triangle where all sides and all angles are unequal

14.     Right triangle <http://en.wikipedia.org/wiki/Right_triangle> or right-angle triangle- the triangle that has a right interior angle

.        Hypotenuse- The side opposite to the right angle is the hypotenuse <http://en.wikipedia.org/wiki/Hypotenuse>; it is the longest side of the right triangle

.        Legs- The other two sides of right triangle are called the legs

.        Oblique triangles- Triangles that do not have an angle that measures 90°

18. Acute triangle or acute-angled triangle.- A triangle that has all interior angles measuring less than 90°

19.     Obtuse triangle or obtuse-angled triangle- A triangle that has one interior angle that measures more than 90°

20.     Quadrilateral - A quadrilateral is a polygon <http://en.wikipedia.org/wiki/Polygon> with four sides (or edges) and four vertices or corners

21.     Parallelogram <http://www.mathsisfun.com/geometry/parallelogram.html>- a quadrilateral, which opposite sides are parallel and equal in length

22.     Rectangle <http://www.mathsisfun.com/geometry/rectangle.html>- a quadrilateral, which has four right angle <http://www.mathsisfun.com/rightangle.html>s (90°). Also opposite sides are parallel <http://www.mathsisfun.com/geometry/parallel-lines.html> and of equal length.

23.     Rhombus <http://www.mathsisfun.com/geometry/rhombus.html>- A quadrilateral,where all sides have equal length

25.     Trapezoid <http://www.mathsisfun.com/geometry/trapezoid.html>- a quadrilateral, which has a pair of opposite sides parallel

.        Kite- a quadrilateral, which has two pair sides, Each pair is made up of adjacent sides that are equal in length

.        Circle-is two-dimensional shapes that is the set of all points <http://en.wikipedia.org/wiki/Point_(geometry)> in a plane <http://en.wikipedia.org/wiki/Plane_(mathematics)> that are a given distance from a given point

.        Center- A point inside the circle. All points on the circle are equidistant (same distance) from the center point

.        Radius-The radius is the distance from the center to any point on the circle. It is half the diameter.

.        Diameter- The distance across the circle. The length of any chord <http://www.mathopenref.com/chord.html> passing through the center. It is twice the radius

.        Circumference- the circumference is the distance around the circle

.        Chord- A line segment linking any two points on a circle

.        Tangent- A line passing a circle and touching it at just one point

.        Secant- A line that intersects a circle at two points

References

1. Լ.Ս. Աթանասյան, Վ.Ֆ. Բուտուզով <<Երկրաչափութուն 7>> Երևան <<Զանգակ 97>> 2006թ.

2.      Լ.Ս. Աթանասյան, Վ.Ֆ. Բուտուզով <<Երկրաչափութուն 8>> Երևան <<Զանգակ 97>> 2007թ.

3.      Լ.Ս. Աթանասյան, Վ.Ֆ. Բուտուզով <<Երկրաչափութուն 9>> Երևան <<Զանգակ 97>> 2008թ.

4.       <http://www.mathsisfun.com/>

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