right triangles

In the previous post we have discussed about adjacent angles and In today's session we are going to discuss about right triangles. A right triangle in the mathematics can be defined as that triangle in which we have 1 angle equal to the right angle which means that 1 angle is equal to the 90 degree. The right triangles are also sometimes called as the right angled triangles. It should be known that the relationship among the different sides and the angles of any right angled triangle forms the basis for the trigonometry.

Now let us talk about the terminology in the right triangles. In any right angled triangle the side which is opposite to the right angle or we can say the 90 degree angle is known as the hypotenuse whereas the sides which are adjacent to the 90 degree angle are known as the legs of the right triangle. (know more about right triangles, here)

Also when the lengths of the 3 sides of the right angled triangle are the integers then that right triangle is known as the Pythagorean triangle whereas the lengths of the 3 sides are collectively called as the Pythagorean triple.

We all know that in any type of the triangle the area is calculated by multiplying 1 / 2 with the length of the base of that triangle and then multiplying that result with the height corresponding to that base of the triangle. But the case of a right angled triangle is very easy. In any right angled triangle, when 1 leg is considered as the base of the triangle then the other leg gives the height of the triangle. Thus the area in any right angled triangle can be calculated by just multiplying 1 / 2 with the product of the lengths of the 2 legs of the triangle.

In order to get more help in understanding the topics: right triangles, Equation for Force and icse board papers 2013, you can visit our next article.

adjacent angles

We say that the angle is formed when we have two rays going in the different directions and they have a same starting point called the vertex. The measure between the two rays is done in the terms of degrees. So we say that the angles are measured in degrees.

 Let us now look at the adjacent angles. The pair of angles formed such that :

a)    The two angles have a common vertex.

b)    The two angles have one  common arm and two uncommon arms.

c)    The common arm exist in between the uncommon arms.

If all the  above three conditions are satisfied , then we say that the pair of angles is called the adjacent angles.

In case the pair of adjacent angles are supplementary, then we conclude that the two uncommon arms of the adjacent angles form a straight line. Thus if the sum of the two adjacent angles  is supplementary, then we say that the two uncommon arms is in fact the straight line.

The reverse of the above statement is also true, which says that if the two adjacent angles are formed on the straight line, then the pair of angles are supplementary.

 We also call these pair of angles as the linear pair of angles.

So by the term linear pair, we simply mean the pair of the adjacent angles which are formed on the straight line and so the sum of this adjacent pair of angles is automatically 180 degrees.

To learn about the  Kinematics Equations, we can take the help of online tutors. These online math tutor can be used any time on your pc without any cost.  icse books free download can also be done by internet when ever required. All you need to have is the P.C. and an internet connection.

Equation of Circle

In mathematical geometry, a round shape in which all the points on the boundary are at same distance from the center is known as a circle. The general Equation of Circle is given by: S 2 + T 2 = r2, where ‘r’ is the radius of a circle (Here S is along to the horizontal axis and ‘T’ is along the vertical axis). All of the points on the boundary of a circle are at fixed distance from the center is known as the radius of a circle. The general equation for circle is given by: (know more about Circle, here)

⇒ (x – s)2 + (y – t)2 = r2;

Now put the value of s, t, and r is 4, 5, 6 respectively then we get:

⇒ (x – 4)2 + (y – 5)2 = (6)2; on further solving the equation of a circle we get:

⇒ x2 + 16 – 8x + y2 + 25 – 10y = 36; So the equation of a circle is:

⇒ x2 + y2 – 8x – 10y + 41 = 36; we can also write it as:

⇒ x2 + y2 – 8x – 10y – 5 = 0; This is the required equation of a circle.

Here we can also write the general form of a circle using the constant value in place of numbers. So the equation of circle using constant is given by:

⇒ x2 + y2 + Sx + Ty + U = 0, here we will also see the equation of a unit circle. We know that ‘1’ is the radius of unit circle, if the radius of a unit circle is more or less then ‘1’ then the circle is not unit circle. The general equation of a unit circle is given by:

⇒ x2 + y2 = 1; let’s discuss how to graphing linear equations. In mathematics there are many methods through we can easily plot the graph of linear equation. To study more about the linear equations go through the online tutor of tamilnadu board of higher secondary education and In the next session we will discuss about adjacent angles. 

isosceles triangle

By the term triangle we mean that it is a closed polygon which if formed by joining 3 line segments. There are different types of triangles based on the lengths of the line segments.

They are : Equilateral Triangle,  isosceles triangle, and scalene triangles. By the term Isosceles triangle, we mean that the triangle which has a pair of the two sides equal. In such a triangle, if we have pair of the  sides equal, we say that the pair of the angles which are formed by the  pair of sides is also equal.  So we come to the conclusion that in the isosceles triangle we have two sides equal and two angles equal. (If you want to get more information about isosceles triangle, Refer this)

If we drop a perpendicular from the angle which is unequal in the isosceles triangle, we observe that this perpendicular is the perpendicular bisector to the line segment which is opposite to this angle. Thus we also called this line as the median of the isosceles triangle.

We further observe that this median, which is also the perpendicular bisector is the line of symmetry of the given isosceles triangle. Any isosceles triangle has only one line of symmetry and this line of symmetry divides the  given isosceles triangle into two equal halves. We also call it the mirror half of the triangle.  On the other hand an equilateral triangle has 3 lines of symmetry and a scalene triangle has no line of symmetry.

If we need to learn about  What are Perpendicular Lines, we can visit the online math tutorial and take the help of the modules based on the above topic in the tutorial. We also have cbse syllabus 2013 online which can be downloaded to understand the pattern of the question paper in the upcoming examination. It guides the students to  know about the important questions  for the exams and In the next session we will discuss about Equation of Circle.

supplementary angles

Angles are formed when we have two rays going in the different directions such that they have the same vertex. The pair of angles is called a supplementary angles, if we have the sum of the two angles equal to 180 degrees.  Thus simply if we say that the given angle is x degrees, then the supplementary of the given angle will be 180 – x degrees. (want to Learn more about supplementary angles, click here),

So if we have any angle say 110 degrees, then the supplement of the given angle 110 will be 180 – 110 = 70 degrees.

 Thus we say that the  supplementary of 50 degrees will be 180 – 50 = 130 degrees.

 Now if we want to know the measure of the angle which is equal to its own supplementary, then we will proceed as follows :

 Let the angle measure be x, then its supplementary angle will be 180 – x degrees.

 Now if we say that  both the angles are of the same measure, then we write it mathematically as follows :

X = 180 – x

On adding x on both the sides we will get :

X + x = 180 – x + x

Thus the above given equation becomes :

2 * x = 180 degrees

Now we will divide both the sides of the equation by 2 and we get :

2 * x / 2 = 180 / 2

Or x = 90 degrees.

Thus we say that the angle 90 is such that it is equal to its own supplement angle.

In order to learn about How to Find Slope of a Line, we can take the help of online math tutorials.  icse guess papers 2013 are also available online, which can guide the students to understand the  concept and the patterns of the question papers in the fore coming  board examinations and In the next session we will discuss about  isosceles triangle.

Parallel Lines

Before going to discuss anything about the parallel lines we should first have an understanding of the term parallelism. The term parallelism is generally used in the geometry which is referred as a property in the space of the Euclidean of 2 or more than 2 lines or the planes or any combination of lines and planes.

We can say that in a plane any 2 lines are said to be parallel if their intersection does not happen or if they do not touch each other at any point. This definition can also be frames in another way as follows. The lines are said to be parallel when their plane is the same and they exist at the same distance in the complete length of the lines. By this we mean that it does not matter at all that how long we are extending the lines, if they are parallel then they will not meet ever. (Know more about Parallel Lines in broad manner, here,)

Now let us discuss about how we show any two parallel lines. For showing that any 2 lines are parallel we make use of the parallel sign which is represented by ||. Thus if we write EF || GH then it means that the line EF is parallel to the line GH.

Let us now pay some attention on the construction of the parallel lines. Suppose we are given a line say x and a point p and we have to construct a line y parallel to the x through the point p. We can make this line y by considering the fact that it should have the same distance from the line x everywhere. There is another way to draw the line y that is we have to consider a random line passing through the point p and crossing the line x at point q. Then we have to take this point q to the infinity.

In order to get more help on the topics: Parallel Lines, College Algebra Problems, icse board papers 2013, you can visit our next article and In the next session we will discuss about supplementary angles.

What are Lines in Geometry

In the previous post we have discussed about Perpendicular Lines and In this blog we are going to discuss about Lines in mathematical world. As we know that slope of a line is generally the measure of an angle of a given line from the x-axis or Y-axis. Here we are going to deal with line in the coordinate plane geometry. In coordinate plane the two lines are present which are vertical and horizontal line. The line whose x- coordinate remains unchanged and y –coordinate changes according to the given values is known as vertical line. A line which move up and down and that line is also parallel to the y – axis of the coordinate plane is known as vertical line. There is no slope defined for vertical line. Equation of a vertical line is given by: x = s. (want to Learn more about Geometry, click here),

A line whose y- coordinate remains unchanged and x – coordinate changes according to the given coordinates is known as horizontal line. A line move straight left and right and also parallel to the x – axis of the coordinate plane is known as horizontal line. The slope of a horizontal line defined as zero. The equation of a horizontal line is given by: Equation of a line is y = t; here the value of 'y’ represents the coordinates of any point on the line and the values of ‘t’ represents the line which crosses the x – axis. Let’s see how to solve equation of Lines in the Coordinate Plane. In mathematical geometry math problem solving is a tool which is used to set a given procedure and see what and when these given procedure should apply. If we want to identify the procedure then it is necessary to know the situation of problem. Before entering in the examination hall please go through the iit sample papers, it helps to solve the problem very easily. This is all about lines and other related topics.

Perpendicular Lines

Hi friends, here in this blog we are going to understand an important topic that is Perpendicular Lines. If we have two lines and these lines make the angle of 90 degree with each then the lines are said to be Perpendicular Lines.

Let we have two lines then the slope of one line is negative to the other line. When the slope of one line is ‘s’ then the slope of other line is = -1 / s. let's see how we construct perpendicular lines in geometry.

To plot the perpendicular lines we have to follow some steps, we have to discuss each step one by one.

Step1: To graph perpendicular lines first of all we take a line of any length.

Step2: Then we have to put a point on the line and the point is named as ‘P’.

Step3: For the construction of perpendicular lines we need compass.

Step4: Then using the compass we make an arc on both side of point ‘P’ and both the arc named as ‘U’ and ‘V’.

Step5: Now we have to put the compass on point ‘U’ and measure the length of compass greater than the point ‘P’.

Step6: Then from point ‘U’ make an arc on the upper side of a line.

Step7: Then with the same length we have to make an another arc from point ‘V’ to the upper side of a line. Both arc cross each other.

Step8: Then using pencil we have to draw a line which meets at the cross point.

And we get another line which is perpendicular to the given line and that line makes exactly 90 degree angle to the other line.

We get this figure when we follow all the above steps:

For the pre algebra practice we have to study the different topics in algebra which are number, fractions, factoring, mixed etc. To get good result please focus on sample papers for cbse board and In the next session we will discuss about What are Lines in Geometry.