Geometry: introduction and general concept
Geometry is a term that is made from the amalgamation of two greek terms that are geo which means earth and metron that means to measure. This term thus could be used to term the measurement of the earth. Geometry is a field of mathematics that deals in study of different patterns, sizes, shapes and figures. It also deals in the configuration of different geometrical objects like points, circles and lines. Geometry is recognized as one of the most developed as well as one of the oldest sciences that includes the theories of many mathematicians till date. The study of geometry involves both analytical as well as creative skills. It prepares a base for the students’ critical thinking. Because of the importance of critical and analytical thinking in our life and to strengthen it, geometry and mathematics are taught to the students from a very early stage of their lives.
But because of its complexity, it is really difficult to understand the concepts of the subject easily. There are many concepts and aspects of geometry that is impossible to understand without proper support and guidance. In order to provide the student with proper assistance to make them complete their assignment by providing them geometry assignment help. The geometry assignment help is an effort to provide the student with the assignment help online that helps them to score better grades.
It is really important for the student to study geometry as it is really important for better understanding the concepts of sizes and shapes that we come across in our daily lives. It also helps the student in analyzing and studying the space and its relationships. It not only clears the concepts of position and space but it also deals in the study of various solids, shapes surface, lines etc. That is all which is present around us. In other words we can say that study of geometry is concerned with everything that surrounds us which has some shape, size or even a line.
It is really important to quote here that geometry is a subject that helps in making both sides of our brain aligned to each other. As we already know that our brain consists of two halves that are left and right. Our left brain is responsible for all the logics and arguments where as our right brain is responsible for all the creative and artistic works.
Because of geometry we can take help of both sides of our brain and create something symmetrical and creative.
It should be noted that there are many other boons of learning and studying geometry but we don’t have access to every concept of geometry. We only have a limited amount of knowledge regarding different concepts of geometry.
Geometry assignment help: importance
Geometry is a field that requires students’ full determination and devotion towards the subject. But there are many concepts of geometry that are really difficult to understand without any proper knowledge and guidance. Many students feel reluctant towards the implementation of geometrical postulates and theorems and thus it becomes essential for the student to seek online help to complete and prepare their assignments on time. The geometry assignment help is an effort done for the students to help them understand different postulates and theorems and their practical implementation. It is really difficult for the student to apply the postulates and theorems and complete their assignments. To reduce their stress and burden they often seek geometry
Postulates and theorems that play a significant role in seeking online geometry assignment help
Geometry could be easily understood if you have proper knowledge of properties and concepts of mathematics as well as the practical implementation of postulates and theorems. The difference between the postulates and theorems are:
- Postulates refer to those statements of geometry that are yet to be proven by logical reasoning and argument but it is already considered true on some grounds.
- Whereas, theorems refer to those statements that are already proven and are true on the basis of other theorems and reasoning.
There are many students who are unable to implement or apply these theories, postulates and theorems. This is the main reason why many students seek online geometry assignment help.
Geometry: angles and lines
It is really important to know about angles and line as it is the base of geometry. In order to make your base strong, it is really important for the students to go through various angles and lines.
Angles could be defined as the resultant of the meeting of two different rays at a common points also known as vertex.
Four properties of angles as provided in geometry assignment help are as follows:
- Reflexive property of equality
In this property of angle, a quantity is related to itself only.
- Addition property of equality
In this property of angle, if, a=c, then, a+b=c+b
- Symmetric property of equality
In this property, if, a=b then b=c
- Transitive property of equality
In this property, if z=x and u=x then z=u
- Addition angle postulate: Under this postulate, if any point falls inside the interior part of the angle, then the sum of two angles with same vertex would be equal to the previously stated angle.
For example: in the figure provided below, point ‘a’ lays in the interior side of the angle qrs. According to the addition postulate, it could be seen that angle qrt+ angle trs.
- Corresponding angle postulate: Under this postulate, if a transversal line intersects a pair of parallel lines, then the corresponding angles would be equal to each other.
It should also be written as when a pair of line gets intersected by a transversal line, and then also the corresponding angles would be equal and lines would be parallel to each other.
- Parallel postulate: Under this postulate, if both a line and a point are given, with the condition that the point is not posted on the line. In such a case there would only one unique line which will not intersect the drawn line at any point and it would pass through that point which is perpendicular to the parallel line.
This postulate draws a distinction between non euclidean and euclidean geometry.
As you can see in the figure provided below that there are many lines that intersect the point ‘e’ but only one of them is parallel to the line cd as it is the only line that would not intersect the line cd at any point.
Angle theorems could be of many types. Some of them are provided by our experts in geometry assignment help.
- Alternate exterior angle: This angle theorem provides that if there is a pair of parallel lines and a transversal is passing through it, then the pairs of alternate exterior angles would be equal to each other.
It can also be written conversely, that is, if a transversal line is intersecting two lines and their alternate exterior angles are equal then, the lines would be parallel.
You can better understand the above concept in the figure provided below.
- Congruent supplements theorem: This theorem applies in the case where two angles are supplementary to two other angles that are equal to each other.
- Congruent complementary angles: This theorem applies in the case where two angles are complementary to two other angles that are equal to each other.
- Right angle theorem: This theorem states that all the right angles would always be equal no matter it is provided in a figure or shown independently.
- Interior angles on the same side theorem: This theorem applies in the case where a transversal intersects a pair of parallel lines, and then the interior angles would always be complementary to each other.
This could also be written conversely, that when a transversal intersects two lines and there interior angles become complementary to each other, then the lines would be parallel to each other.
It should be noted here that sum of these angles would always be 180?.
- Vertical angle theorem on the same side: This theorem states that if two angels are vertical to each other, then they would always be equal to each other.
Triangles could be recognized as three sided closed figure. It could be of various types. Our experts provide different congruency rules that could make two triangles congruent to each other in geometry assignment help.
- Sss congruency rule (side-side-side): If in a triangle, the three sides are equal to the sides of another triangle, then the two triangles would be congruent to each other.
- Sas congruency rule (side-angle-side): If in a triangle, two sides and the angle between them are equal to two sides and angle between them of another triangle then they both would considered as congruent triangles.
This could be better understood by the following diagram.
- Asa congruency rule (angle-side-angle): If in a triangle two angles and the side included in it, of the one triangle are equal to the two angles and side of another triangle then both of them would be considered to be congruent to each other.
- Aas congruency rule (angle-angle-side): If in a triangle two angles and a side not included in the angles are equal to the angles and side not included in them, then both the triangles would be congruent to each other.
Parallelogram: Parallelogram could be referred to a four sided figure in which both pair of sides are parallel to each other. It should be noted here that the sum of interior angles of a parallelogram is equal to 360?.
Properties of a parallelogram
Some properties of a parallelogram are provided in geometry assignment help by our experts.
- Both pairs of lines in a parallelogram are equal to each other that is ab=cd and bc=da.
- Likewise, both the pairs of the angles are also equal to each other, that is ?a = ?c and ?b = ?d.
- The diagonal of a parallelogram would always bisect the angles into two halves.
- A diagonal would also divide the parallelogram into two congruent triangles that is,
Diagonal ac would divide the parallelogram into two congruent triangles i.e. ?abc and ?dab.
- Area of a parallelogram could be calculated by the given formula
Ab * height of the parallelogram
Dc * height of the parallelogram
Calculation of area of a polygon and green’s theorem: This is one of the most common ways of calculating the area of a polygon. Green’s theorem refers to the method of measuring the area of a polygon by breaking the polygon into smaller segments. By doing this, the areas of the smaller segments are calculated to derive the area of the polygon.
However, it is really difficult to use this theorem as sometimes when the shape of the figure is not provided physically, it becomes impossible to break the polygon into smaller segments.
Polygon: simple formula
Because of the complexity of the green’s theorem, the area of a polygon could also be calculated through a very simple formula that is
It should be noted here that, in order to apply the formula you must possess the necessary information about the coordinates.
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