Basic Geometry

In this chapter, we will define a reasonable number and verity of plane figures relating with physical object. Suppose, one of the most common physical plane figures in the plane surfaces of objects as top of oval tea table are the examples f plane physical objects. Such physical objects could be represented by the class of figures that could be cut, each in one piece, from flat sheets of paper. Some plane figures are given below. These above plane figures have any kind of properties which associate with the physical paper figure. Observing the above plane figure. we get "all in one piece" like its corresponding paper figure, and there exist a class of set (May be set of points or set of lines) if they are not hollow. Now we denote this class of sets by S: Although the figures are "all in one piece", all are not the plane convex figure. So, defining the plane convex figure, the sets must be planar nonlinear, bounded and convex. Any physical objects has an actual

A quadrilateral whose opposite sides are parallel is called a Parallegram. Properties of a parallelogram *Opposite sides of the parallelogram are equal. *Opposite angle of the parallelogram are equal. *The diagonals of the parallelogram bisect each other (I) Rectangle: Rectangle is a types of parallelogram but parallelogram is not rectangle because all angle of rectangle equal each other or all angle of rectangle equal to 90 degree. The diagonals of rectangle are equal. (II) Square: Square also a types of parallelogram but parallelogram and rectangle are not square because all side and angles of square are equal to each other. The diagonals of square are equal.

Types of triangle Three straight line intersect to each other there are make triangle. Triangle is a closed set, there are three angle and three side. Types of triangle according to side -Isosceles triangle -Equilateral triangle -Sealant triangle Types of triangle according to angle -Acute angle triangle -Right angle triangle Obtuse angle triangle Some theorem of triangle *Some of angle of triangle is 180 degree. *Base angles of an isosceles triangle are equal. *Each of the base angles of an isosceles right triangle is 45 degree. *An exterior angle of a triangle is greater than either remote interior angle. *If two sides of a triangle are unequal, the angles opposite them are unequal and the larger angle is opposite the longer side. *The sum of the lengths of any two sides of a triangle is greater than the length of the third side. *In a correspondence of right triangles, if the hypotenuse one corresponds and is congruent to that of the other and if one pair of corres

(I) Angle formed by intersection each other lines -Vertical opposite angle - Adjecent angle Straight angle -Complementary angles -Supplementary angle (II) Angle formed by a transversal with the parallel lines -Alternative angles When a transversal cuts a pair of lines then, *Both interior *Both non adjacent *Both either side (II) Co-interior angle when a transversal line cuts a pair of lines then the interior angles on the same side of the transversal are called co-interior or consecutive interior angles. (III) Corresponding angle If a pairs of lines is intersected by a transversal line, then the pair of non adjacent interior and exterior angle formed on the same side of it are called corresponding angles.

This solid polyhedron is a convex solid whose boundary is the union of a finite number of full polygons, no two of which are coplanar. The full polygons are the faces of the polyhedron; the edges of the polyhedron are the sides of the polygons and the vertices of the polyhedron are the vertices of the polygons. A segment that joins two vertices and is not in a face of the polyhedron is a diagonal of the polyhedron. A dihedral angle between two face-planes and containing two of the faces is a dihedral angle of the polyhedron. The angles of the polygons in the faces are plane angles or face angles of the polyhedron. -Regular polyhedron: A regular polyhedron is a geometric solid, all of whose faces are congruent regular polygons, in which the same number of polygons meet at each vertex or a regular polyhedron is a polyhedron whose faces are congruent regular polygons and each two of its dihedral angles are congruent. The famous Swiss mathematician Leonhard Euler, was found the there ar

In arithmetic we learn that one method of comparing two quantities in respect of their magnitude is to express them in the form of a fraction the numerator and denominator of which state the sizes of the quantities measured in suitable and the same units. This form of comparison is called a ratio. Hence we speak of the ratio of two straight lines, we mean the ratio of the numbers which express the measures of their lengths in terms of the same unit. Similarly, by the ratio of the areas of two triangles we means the ratio of the numbers which express these areas in the same square units. Similar Triangles:- The two triangles, however, have the same shape one might be considered an enlargement of the other. Such triangle are called similar triangle and to indicate this, we write triangle ABC similar to triangle DEF. This notation indicates a special correspondence between the vertices of the two triangles, just as the notation used for congruence does. - Two triangles are similar iff

the angle between a straight line and a plane the angle between the straight line and its projection on the plane. Consequently the projection of a straight line op on a plane which it meets at O

All of the above coin are identical in their shape and size. If tracing were made of one of tem, it could be placed so as to coincide exactly with any of the others. Such figures are said to be congruent. Such a correspondence is called a congruent between the two triangles and is represented by the symbol …… Some theorem of congruence triangle I. If the three sides of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent. II. If two sides and the included angle of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent. III. If two angles and the included sides of one triangle are equal to the corresponding parts of another triangle, then the triangle, then the triangles are congruent. IV. If correspondence of two triangles or of a triangle with itself such that two angles and the side between them are respectively congruent to the two corresponding angles and the side between them,

Foundation of geometry is the study of geometric system that can be constructed in a special fields of mathematics. The word "foundation" can be judged from two different facts. First is the mathematical representation of the geometric nature of physical space that, we want represent mathematically entire of the universe. Second is the system standing by itself, which we can not study and property of a geometric figure in our space until we have established the space, have defined both the property and the figure, and have shown that the figure actually exist in the space. Before we began formal mathematics it is necessary to understand the nature of foundation properties. Some of the main foundation properties are given below. (I) Existence Property An existence property always states that there exists some figure with a given property. The property also states that how many of these figures are there in the system. When theexact number is one then the property is called a

Geometry is the branch of mathematics. It has been interlocked with many other subjects and different kinds of human activities. As the sets of numbers are the building blocks of Arithmetic and Algebra, sets of points are building blocks of Arithmetic and Algebra, sets of points are geometric ideas that cannot be seen or touched, but many things in everyday life are good approximations of these ideas. Geometry is related to Physical objects and to the experiences of sight and touch. It is a system of ideas, that geometric facts are obtained by reason rather than by observation and that geometry is a matter of logic. These two different above mentioned points of view are two worlds of geometry i.e. Physical and Mathematical. Physical geometry deals with the actual measurements, directly of indirectly, of those properties of physical objects that relate to such idea as distance, angle, size and shape. The word 'Geometry' is derived from two Greek words 'Geo' and 'Me