Presentation on theme: "Geometry is axiomatic-deductive system is very strict, and has developed very rapidly. Geometry objects are objects that abstract thoughts. Understanding."— Presentation transcript:
Geometry is axiomatic-deductive system is very strict, and has developed very rapidly. Geometry objects are objects that abstract thoughts. Understanding the geometry is a point. Object geometry is part of mathematical objects. Geometry objects among others points, lines, ray lines, segments, angles, triangle, parallelogram-parallelogram, circle, elllip, parabolic, cube, pyramid, tubes, balls, elipsoida, hiperboloida, hyper paraboloida. Geometry objects in one-dimensional plane (R), is a geometric object that is the number lineamong others can be a point, line segment, ray line, and the set point as ray line but without end point, which we can call the "ray line without a endpoint / starting point " DEFINITION OF GEOMETRY
Point is location, no length, width or height. A point is an idea, or abstraction. Since a point cannot be defined using simpler terms, it is an undefined term. POINT
Line is unlimited length, straight, no thickness, no endpoints. A line is an idea or abstraction. Since a line cannot be defined using simpler terms it is an undefined term. LINE
Plane is no boundary, continues in all directions, flat, no thickness. A plane is an idea, or abstraction. Since a plane cannot be defined using simpler terms, it is an undefined term. PLANE
Space is no boundary, length, width, and height. Space is an idea, or abstraction. SPACE
Segment is a line which has the set of points. A segment is an idea, or abstraction. Since a segment cannot be defined using simpler terms, it is an undefined term. SEGMENT
It is possible that the world of nature provided humans with their first notions of geometry.There are many example of geometric shapes in the physical world.Over the centuries people began to classify the shapes.They gave them names and created definition in order to describe the things they saw. We often look for relationship between two or more geometric figures.We say thee point are collinear (lie on one line) two lines are parallel (do not meet) or two angles are congruent (are the same size) write the letter of each picture that suggest a relation and name the relationship suggested.
We draw dots on paper to represent points capital letters beside them name the points.We call points A, B and point C We can think of a line as a set points by labeling a pair of points we can name the line in terms of two points.For example points A and B are on the line so we call it AB.We assume that only one line goes through both A and B.Another way of saying this is,Two points determine a line,sometimes a line labeled by using one small letter.Here line AB can also be called line L A pline can also be through of as a set of points a plane is named either by placing a single letter by the plane or by naming a set of three points on the plane that are not all on the line.We say plane N or plane ABC We assume that only one plane contains the three points we say that three points not all on line determine a plane.When thingking of line L as aset of points we can say point A is on line L and point A is an element of line L to describe the same situasion we can also say line L contains point A If A,B,C are points of line L as shown in the figure we say point B is between points A and C. If A,B and C are not all the same lines we donot use between to describe their relations :D RELATIONS AMONG POINTS,LINES AND PLANES
A angle is the union of two noncollinear rays which have the same endpoint. ANGLE
A triangle is the union of two three segmen determined by three noncolinear points. TRIANGLE
A Quadrilateral is the union of four segmenys determined by four points, no three of which are collinear. The segmens intersect onli at their endpoints. Quadrilateral
A circle is the set of all points in a plane that are a fixed distance from a given point in the plane. CIRCLE
Definition An angle is the union of two noncollinear rays which have the same endpoint.