Right Angle Triangle Properties for SSC Exams

Right Angle Triangle Properties

We know that in Right Angle Triangle properties A shape that has three sides Is called Triangle and sum of all angle is 180 degree but A right-angled triangle has one of its interior angles equal to 90 degrees.

Also the longest side ( hypotenuse ) is always opposite to the right angle ( 90°)

The right triangle plays an important role in SSC CGL and SSC CHSL exams.

Let us learn more about right Angle triangle in this article. 

Pythagorean Triples or Triples of Right angle Triangle

We know that the expression a² + b² = c² is a pythagoras theorem which is important or Standard Right Angle Triangle property. 

The possible numbers of a, b and c is Pythagorean Triples provided that the three possible number must be positive integers.

Here, c is the hypotenuse, a is the perpendicular and b is the base of the right-angled triangle.

How to find Pythagorean Triples

The standard formula for Pythagorean Triples is Pythagoras Theorem but it only identifies the numbers is correctly fit in Right Angle Triangle properties rather then to discover.

For this purpose we have a short trick which will help us to discover the remaining 2 Pythagorean

Triples if we have one.

Pythagorean Triples can be found by two ways. First is for even numbers and second is for odd numbers.

We need to follow these steps to find pythagorean triples

Even number

Step 1   let suppose we took 8 and then we have to sequre the number which is 64.

Step 2   Divide number 64 by 4 and them we get 16

Step 3  Subtract and Add number 1 from number 16 and add 1

Step 4   Possible numbers are 15 ( 16 - 1 )and 17 ( 16 + 1 ) and we get pythagorean triples ( 8, 15, 17)

Odd number

Step 1   let suppose we took 3 and then we have to sequre the number which is 9.

Step 2   divide number 9 by 2 and them we get 4.5

Step 3   Subtract and Add number 0.5 from number 4.5

Step 4   Possible numbers are 4 ( 4.5 - 0.5 )and 5 ( 4.5 + 0.5 ) and we get pythagorean triples ( 3, 4, 5)

Pythagorean Triples List

(3, 4, 5)	(12, 35, 37)	(36, 77, 85)
(5, 12, 13)	(16, 63, 65)	(39, 80, 89)
(8, 15, 17)	(13, 84, 85)	(48, 55, 73)
(7, 24, 25)	(20, 21, 29)	(65, 72, 97)
(9, 40, 41)	(11, 60, 61)	(28, 45, 53)

Properties of right angle triangle

Being a candidate preparing for SSC CGL and SSC CHSL exams. we have to prepare those topic strong that take higher weightage in Right Angle Triangle Properties.

Formulas given below is very important because major questions were based on these formulas in previous exams. 

BC² = FC × AC 
AB² = AF × AC
BD² = AD × DC

Let suppose AF and FC are in proportion of p and q then 

`frac{AF}{FC} = \frac{p}{q}`

Or

`\frac{AF}{FC} = \frac{D²}{E²}`

Or

`\frac{p}{q} =  \frac{D²}{E²}`

Relation of side BF with other sides

BF = `\sqrt{pq} = \frac{D\times E}F`

`\frac{1}{BF²}  = \frac{1}{D²} + \frac{1}{E²}`

Area of Right Angle Triangle 

the standard formula for Area of Right Angle Triangle is Area = 1/2 ( base × perpendicular) similarly some other important alternatives are mentioned below that often comes in exams. Basically all these formulas are derived from standard formula.

Area = r × s
here
r = radius of incircle or inradius
R = radius of circumcircle or circumradius

Area = a × b
here
a = AD
b = DC

Area = r² + 2Rr
here
r = radius of incircle or inradius
R = radius of circumcircle or circumradius

Area = (S - H)S
here
s = P+B+H/2
H = Hypotenuse or H = 2R

After examine Right Angle Triangle Properties you how to prepare for SSC exams. 

SSC exams easily be cracked in very first attempt provided that we are focusing on relevant topics. 

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