Types of Triangle and Center for SSC CGL

• Types of Triangle
• Important Angle Properties
• Centre of Triangle
• Right Angle Triangle

Geometry section of maths contains 3 - 4 questions in SSC CGL and SSC CHSL exams.

It is important to learn all concepts and formulas of Geometry.

Here i will provide you some important concept that frequently asked in all SSC and Railway exams.

Triangle

A shape that has three sides Is called Triangle 

• Sum of all angle is always 180°

Types of Triangle

1. Acute angle Triangle

Properties of Acute angle triangle

Square of two sides always greater than remaining = 6² < 5²+4²

2. Obtuse angle Triangle

Properties of Obtuse angle triangle

Secure of two sides always less than remaining = 7² > 3² + 4²

3. Right angle Triangle

Properties of Right angle triangle

Sequare of two sides always equal than remaining ( Pythagorean theorem ) = 3² + 4² = 5²

Important angle properties 

If Line A and Line B are parellel then

1. Alternate angles always equal

ㄥ3 = ㄥ6 ,

ㄥ4 = ㄥ5 

2. Vertical angles always equal

ㄥ1= ㄥ4 ,

ㄥ2 = ㄥ3,

ㄥ5 = ㄥ8,

ㄥ6 = ㄥ7

3. Corresponding angles always equal

ㄥ1 = ㄥ5 , 

ㄥ4 = ㄥ8 , 

ㄥ2 = ㄥ6, 

ㄥ1 = ㄥ5

Other important fact = ㄥ4 + ㄥ6 = 180°

Center of Triangles

1. Incenter 

 Incenter is a point in which the three bisectors of angle A, B, and c of a triangle intersect.

Properties of Incenter

• ㄥBIC = 90° + `\frac{A}2`

  ㄥCIA = 90° + `\frac{A}2`

  ㄥBIA = 90° + `\frac{A}2`

• FI = EI= DI

• let Radius of Incircle or Inradius ( r )

         Semiperimeter (s)

r = `\frac{area of triangle}s`

r = `\frac{median}3` = `\frac{height}3` = `\frac{angle bisector}3`

• If AD = h1
      BE = h2
      CF = h3

`\frac{1}r = \frac{1}{h1} + \frac{1}{h2} + \frac{1}{h3}`

Inradius of Equilateral triangle
r = `\frac{a}{2\sqrt3}`

( a = side of Equilateral triangle)

• Inradius of right angle triangle

r = `frac{P + B - H}2` 

2. Circumcenter

Properties of Circumcenter

• OA = OB = OC = R = Circumradius

• ㄥBOC = 2ㄥBAC

• `\frac{a}SinA=\frac{b}SinB =\frac{c}SinC = 2R`

• `R = \frac{abc}{4\times area\;of\;triangle}`

3. Orthocenter

Properties of Orthocenter

• Area of triangle =

 `\frac{a×h1}2 = \frac{b×h2}2 = \frac{c×h3}2`

• h1 : h2 : h3 = `\frac{1}a : \frac{1}b : \frac{1}c`

• ㄥBHC = 180° - ㄥA

• `\frac{AB+BC+CA}{AD+BE+CF}` > 1

• `\frac{h1h2}{h1+h2}` < h3 < `\frac{h1h2}{h1-h2}`

4. Centroid

Properties of centroid

• AG : GD = 2 : 1

• AO : OG : GD = 3 : 1 : 2

• Area of GEF = `frac{1}12` × Area of ABC

• AB² + AC² = 2 ( AD² + BD² )

Right Angle Triangle 

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

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

`\frac{AF}{FC} = \frac{D²}{E²}`

BC² = FC × AC 

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

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