Triangles:
Out of many geometrical structures, triangle is one of the basic shapes of geometry. Triangles are polygons having 3 sides or edges, which are nothing but line segments and 3 angles or vertices, which may be of same measures sometimes (for quick solution also try area of equilateral triangle calculator). The sides are termed as A, B, C and triangle is represented as Δ ABC.
As all grade XI board of intermediate education Andhra Pradesh students are aware, triangles are classified according to the lengths of the three sides:
1. Isosceles triangle: Here, two sides are same in length and two angles which are opposite to the sides of same length are same in measure.
2. Equilateral triangle: All sides are equal in length and all three angles are same measuring 60 0 each (as total interior angle in a triangle is 1800) in case of equilateral triangles.
3. Scalene triangle:All sides are different in length and all three angles are different in measure in case of scalene triangles.
Triangles are also classified according to the angles of three sides (for more on triangles visit this):
1. Right angle triangle:These triangles has one of its interior angle measuring 900 . In case of right triangles, special names are given to each side of the triangle, with the side which is opposite to the right angle being termed as hypotenuse, which is the longest side of the right triangle and the other two sides being known as the legs.
2. Acute angle triangle: All three interior angles are less than 900 in case of acute angle triangles.
3. Obtuse angle triangle:These triangles have one angle which is more than 900 .
In grade XI you will also be studying one more topic, i.e., special right triangles, which are nothing but right triangles having some specified features which makes calculation easy. There are two types in which special right triangle are being classified: angle based and side based.
In angle based special right triangle, the angles are divided such that the right angle (largest) is equal to sum of the other two angles. There are two types of special right triangle which are angle based:
1. 45-45-90 angle: As you can judge by name, it has 2 angles measuring 450 and one 900 and you can get such triangle by cutting a square diagonally. Here the angles are in the ratio 1 : 1 : 2 and by using Pythagoras theorem(which says - in a right angle triangle, the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the two legs. The theorem is represented by the equation: a2 + b2 = c2, where c represents the hypotenuse, longest side) , the sides are in the ratio of
1: 1 : √2, which means that two sides are equal in length also.
Hence such kind of triangles have characteristic of both the isosceles and the right angle triangles.
2. 30-60-90 angle: This kind of special right triangles are very common and has one 300 ,one 600 and one 900 angle. There is one theorem which applies to these triangles, stated as,
In a 30-60-90 triangle, the length of hypotenuse is two times the length of leg opposite to the 30o angle. And the length of the other leg is calculated as SQRT (3) times the leg opposite to the 30o angle.
Now finally, in side-based special right triangles, the lengths of the sides form ratios of whole number, such as 3 : 4 : 5 ,11 : 12 : 13 etc.
In upcoming posts we will discuss about Probability and Statistics and Congruence. Visit our website for information on Calculating Standard Deviation
Out of many geometrical structures, triangle is one of the basic shapes of geometry. Triangles are polygons having 3 sides or edges, which are nothing but line segments and 3 angles or vertices, which may be of same measures sometimes (for quick solution also try area of equilateral triangle calculator). The sides are termed as A, B, C and triangle is represented as Δ ABC.
As all grade XI board of intermediate education Andhra Pradesh students are aware, triangles are classified according to the lengths of the three sides:
1. Isosceles triangle: Here, two sides are same in length and two angles which are opposite to the sides of same length are same in measure.
2. Equilateral triangle: All sides are equal in length and all three angles are same measuring 60 0 each (as total interior angle in a triangle is 1800) in case of equilateral triangles.
3. Scalene triangle:All sides are different in length and all three angles are different in measure in case of scalene triangles.
Triangles are also classified according to the angles of three sides (for more on triangles visit this):
1. Right angle triangle:These triangles has one of its interior angle measuring 900 . In case of right triangles, special names are given to each side of the triangle, with the side which is opposite to the right angle being termed as hypotenuse, which is the longest side of the right triangle and the other two sides being known as the legs.
2. Acute angle triangle: All three interior angles are less than 900 in case of acute angle triangles.
3. Obtuse angle triangle:These triangles have one angle which is more than 900 .
In grade XI you will also be studying one more topic, i.e., special right triangles, which are nothing but right triangles having some specified features which makes calculation easy. There are two types in which special right triangle are being classified: angle based and side based.
In angle based special right triangle, the angles are divided such that the right angle (largest) is equal to sum of the other two angles. There are two types of special right triangle which are angle based:
1. 45-45-90 angle: As you can judge by name, it has 2 angles measuring 450 and one 900 and you can get such triangle by cutting a square diagonally. Here the angles are in the ratio 1 : 1 : 2 and by using Pythagoras theorem(which says - in a right angle triangle, the square of the length of the hypotenuse is equal to the sum of the square of the lengths of the two legs. The theorem is represented by the equation: a2 + b2 = c2, where c represents the hypotenuse, longest side) , the sides are in the ratio of
1: 1 : √2, which means that two sides are equal in length also.
Hence such kind of triangles have characteristic of both the isosceles and the right angle triangles.
2. 30-60-90 angle: This kind of special right triangles are very common and has one 300 ,one 600 and one 900 angle. There is one theorem which applies to these triangles, stated as,
In a 30-60-90 triangle, the length of hypotenuse is two times the length of leg opposite to the 30o angle. And the length of the other leg is calculated as SQRT (3) times the leg opposite to the 30o angle.
Now finally, in side-based special right triangles, the lengths of the sides form ratios of whole number, such as 3 : 4 : 5 ,11 : 12 : 13 etc.
In upcoming posts we will discuss about Probability and Statistics and Congruence. Visit our website for information on Calculating Standard Deviation
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