Details of Triangle and its Properties

A triangle is one of the basic shapes of geometry.In maths exam papers there are three or four question are given from this chapter.This type of problem are given in Quantitative Aptitude which is a very essential paper in SSC Exams

Definition of Triangle 

A triangle method in a geometry ,a triangle is one of the basic shapes in a polygon with three corners and vertices or three sides and edges which are line segments. A triangle with vertices A, B, and C is denoted triangle ABC.

In other way , A triangle is a closed figure with three sides .It is a polygon with three sides and 3 vertices/corners. Learn about different triangles in details such as equilateral, isosceles, scalene triangles etc. 

•  Based on Sides:

1.Equilateral triangle: A triangle where all three sides are equal is called an equilateral triangle. Each angle in this triangle = 60.  An equilateral triangle is also known as equi angles triangle.

2.Isosceles triangle: A triangle whose two and only two sides are equal is called an isosceles    triangle.  Two angles in this triangle are equal.

3.Scalene Triangle: A triangle whose all angles and sides are different is called Scalene triangle.

• Based on Angles:

1.  Acute angle triangle:  A triangle whose angles all less than 90 degrees is called acute angle triangle 

2. Right angle triangle: A triangle which has one angle equal to 90 degrees is called right angle triangle.

3. Obtuse angle triangle: A triangle which has an angle more than 90 degrees is called Obtuse angle triangle.

• External Angle of a triangle:

The exterior angle x is always equal to sum of the two remote internal angles. i.e.,∠x=∠a+∠b

If two triangles are similar, their sides, their altitudes, their medians are in the same ratio.  The mostly occur condition for similarity is AAA similarity.  

• AAA Similarity of the triangles*:

If all the three angles of a triangle is equal to the corresponding three angles of the other triangle, then both the triangles are similar.

If, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F, then ΔABC ≈ ΔDEF 

Note: While applying the AAA similarity, always look for angles and their corresponding sides in two triangles in the same order.

•  SAS condition of similarity:

If the two sides of a triangle is in proportion with the corresponding two sides of the other triangle and the included angle of one is equal to the included angle of the other, the triangles are similar. AB/DE=BC/ EF then ∠B=∠E  

 then ΔABC≈ΔDEF

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