Showing posts with label Line Segments. Show all posts
Showing posts with label Line Segments. Show all posts

Tuesday, March 12, 2013

Geometry Terms and Definitions

Introduction to learning geometry terms and definitions:
Geometry is a branch of mathematics which  deals with the study of different shapes. Also learning the geometry terms and definitions include certain constructions of geometry such as lines, angles, plane etc., the word geometry is derived from the two words ‘geo’ meaning ‘earth’ and ‘metron’ meaning measuring. The geometry of plane figures are known as Euclidian geometry or plane geometry. I like to share this Skew Lines Examples with you all through my article.


Learning Terms and definitions of geometry:


There are various terms and definitions involved in geometry. Some of the terms and definitions involved in geometry for learning are listed below:

1. Point:

In geometry a point is a location in space with a dot on a piece of paper is known as point.

2. Mid point:

A segment that can be divides into two with equal length are known as mid point.

3. Square:

It has all the sides are equal with angles are equal to 90°. Then their diagonals are equal and they bisect at right angles.

4. Line:

The region where two points connects via the shortest path and continues indefintely in both the directions is referred as a line.

5. Line segments:

In geometry a line segments is a part of a line between the two points.

6. Perpendicular line segments:

If a line segments that intersect or cross at an angle of 90°. Then is it known as perpendicular line segments.

7. Parallel line segments:

If a line segments that never intersect or they can always in the same distance apart is known as parallel line segments.

8. Parallelogram:

The opposite sides are equal and parallel and opposite angles are equal. The diagonals are bisect to each other. Understanding Volume of Rectangular Prism is always challenging for me but thanks to all math help websites to help me out.


Learning terms and definitions of geometry for triangles and circles:


Learning terms and definitions of geometry for triangles and circles includes the following:

1. Right angle:

Angle that measures 90° is referred as right angle

2. Rectangle:

Their opposite sides are equal and parallel with the angles are equal to 90°..

3. Acute angle:

Angle that measures less than 90° is referred as acute angle

4. Obtuse angle:

An angle that measures more than 90° is referred as Obtuse angle.

5. Isosceles triangle:

A triangle with two equal length sides and also with two equal internal angles is referred as an isosceles triangle.

6. Equilateral triangle:

If a triangle has the equal length on all three sides, then it is referred as equilateral triangle.

7. Circles:

A circle has a locus of all points which equidistant from the center of a point.

8. Circumference:

The distance around a circle is called the circumference of a circle.

9. Concentric circles:

If the circles having the same centre but different radii are called concentric circles.

10. Tangent of circle:

If a line perpendicular to the radius, then, it can touches only one point on the circle.

Tuesday, February 26, 2013

How To Solve Geometry

Introduction :

Geometry is a branch of mathematics, which deals with lines, curves, solids, surfaces and points in space. In geometry, a point has a position only and is represented by a dot. A point has no length, width, or thickness. A line has length but no thickness or width. The position of a line with end points are called line segment.


How to solve Geometry Problems:


Geometry Problem 1:

Solve the equation of the straight line parallel to 6x + 4y = 12 and which passes through the point (3, − 3).

Solution:
The straight line parallel to 6x + 4y − 12 = 0 is of the form
6x + 4y + k = 0 … (1)
the point (3, − 3) satisfies the equation (1)
Hence 18 − 12 + k = 0 i.e. k = -6
3x + 2y - 6 = 0 is the equation of the required straight line.

Geometry Problem 2:

Solve the equation of the straight-line perpendicular to the straight line 3x + 4y + 28 = 0 and passing through the point (− 1, 4).

Solution:
The equation of any straight- line perpendicular to 3x + 4y + 28 = 0 is of the form4x − 3y + k = 0
the point (− 1, 4) lies on the straight line    4x − 3y + k = 0
− 4 − 12 + k = 0 ⇒ k = 16
the equation of the required straight line is 4x − 3y + 16 = 0

Geometry problem 3:

The lengths of two sides of right triangle are 7 cm and 24cm. Find its hypotenuses.

Solution:

AC = 7 cm
BC = 24 cm
AB  = ?
AB^2 = 7^2 + 24^2
= 49 + 576
AB^2  = 625
AB = √625 = 25

Thus, the hypotenuses are 25 cms in length.



Geometry Problems to practice:


1) Solve the equation of straight line passing through the points (1, 2) and (3, − 4).

Ans: 3x+y = 5

2) Solve the distance between the parallel lines 2x + 3y − 6=0 and 2x + 3y + 7 = 0.

Ans: √13 units

3) Find the point of intersection of the straight lines 5x + 4y − 13 = 0 and 3x + y − 5 = 0.

Ans: The point of intersection is (1, 2)

4) Solve the equation of the curve formed by the set of all those points the sum of whose distances from the points A (4, 0, 0) and B (-4, 0, 0) is 10 units.

Ans: 9x^2+25y^2+25z^2-225=0.

Sunday, February 24, 2013

Definitions of Geometry

Introduction to definitions of geometry:

"Earth-measuring" is a part of mathematics concerned with questions of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow. A mathematician who works in the field of geometry is called a geometer. Source – wikipedia.


Importants definitions of Geometry :

There are various terms and definitions involved in geometry. Some of them are listed below:

Lines:

In geometry if A and B are the two points in the plane. There is only one line AB containing the points. The region where two points connects via the shortest path and continues indefinitely in both the directions is referred as a line.

Line segments:

Line segment is a part of line between two points. The line Segments that intersect at an angle of 90° is called Perpendicular line segments and the line segments that never intersect are known as parallel line segments.

Angles:

An angle is an inclination between two rays with the same initial point.

Right angle:

Angle that measures 90° is referred as right angle

Acute angle:

Angle that measures less than 90° is referred as Acute angle

Obtuse angle:

An angle that measures more than 90° is referred as Obtuse angle.

Scalene triangle:

A triangle in which all three sides has different lengths is known as Scalene Triangles.

Isosceles triangle:

A triangle with two equal length sides and also with two equal internal angles is referred as an isosceles triangle.

Equilateral triangle:

In geometry if a triangle has the equal length on all three sides, then it is referred as Equilateral triangle.

Axioms:

Certain statements are assumed as being true without proof apart from the theorems. Such assumptions are called axioms.

Complementary angles:

Two angles are said to be complementary if their sum is 90° and each is called the complement of the other.

Supplementary angles:

Two angles are said to be supplementary if their sum is 180° and each is called the supplement of the other.


Important definitions of geometry: Circles


The followings are some of the important definitions of geometry in circles.

Circles:

A and B are two concentric circles with radii r and R respectively and O is the center of the circle.

Circumference:

The distance around a circle is called the circumference of a circle.

Radius:

It is the distance from center of a circle to any point on that circle's circumference.

Chord:

Chord is a line segment joining two points on a curve.

Arc:

Part of a curve is referred as an arc.

Concentric circles:

Circles having the same center but different radii are called concentric circles.

Intersecting circles:

Two circles are said to be intersecting when they cut at two different points.

Touching circles:

In geometry two circles are said to touch one another if they meet only at one point. The point at which they touch one another is called the point of contact.

Monday, November 26, 2012

Line Segments in a Pentagon

Introduction to line segments:

The division of a line with two end points is called a line segment. Line segment RS which we denoted by the symbol `bar(RS)` .



Note: We shall denote a line segment `bar(RS)` by RS only.

From the above figure, we call it a line segment RS. The points R and S are called end-points of the line segment RS.

We can also name it as line segment RS.

A line segments:

(a) A line segment has a definite length.

(b) A line segment has two end-points

Line Segments in a Pentagon:
Find the line segments of the given pentagon. The pentagon shown below figure,



Solution:

Given:

Pentagon EFGHI

To find the line segments in a pentagon:

We know that the line segments are consisting of two end points. Here, the pentagon has five end points, such as E, F, G, H, and I. The five end points to form the line segments in a pentagon by connecting these end points shown in figure, such line segments are EF, FG, GH, HI, and IE. These line segments are represented by `bar(EF)` , `bar(FG)`, `bar(GH)` , `bar(HI)` , and `bar(IE)` . Therefore, the given pentagon has five line segments.Please express your views of this topic Converting Fractions to Percents by commenting on blog.

Line Segments in a Solid Pentagon:

Find the line segments of the given solid pentagon. The solid pentagon shown below figure,



Solution:

Given:

Solid pentagon ABCDEFGHIJ

To find the line segments in a solid pentagon:

We know that the line segments are consisting of two end points. Here, the pentagon has ten end points, such as A, B, C, D, E, F, G, H, I, and J. The ten end points to form the line segments in a solid pentagon by connecting these end points shown in figure, such line segments are AB, AD, AJ, BC, BF, CD, CE, DI, EF, EG, FH, GH, GI, HJ, and IJ. These line segments are represented by `bar(AB)` , `bar(AD)` , `bar(AJ)` , `bar(BC)` ,` bar(BF)` , `bar(CD)` , `bar(CE)` , `bar(DI)` , `bar(EF)` , `bar(EG)` , `bar(FH)` , `bar(GH)` , `bar(GI)` , `bar(HJ)` , and `bar(IJ)` . Therefore, the given solid pentagon has fifteen line segments.