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Triangles

In any triangle:

  •        The sum of any two sides is always greater than the third side.
  •        The difference between any two sides is smaller than the third side.
  •        The sum of the three angles is equal to 180°.
  •        Area ½ × Base × Height  
  •       Area √s(s – a)(s – b)(s – c) Where s = Semiperimeter = (a+b+c) ÷ 2

Right-Angled Triangle

In a right-angle triangle, one of the angles is 90°, and the side opposite to this is known as hypotenuse. In a right-angle triangle, (Hypotenuse)2 = (base)2 + (height)2

 

It is better to remember the Pythagorean triplets by heart. The following triplets are important.

3, 4, 5              5, 12, 13           7, 24, 25           8, 15, 17           9, 40, 41

11, 60, 61 12, 35, 37 20, 21, 29 28, 45, 53

             
          
a    c2 = a2 + b2                       

                                  b                                                   

                                                                              

                                                       

 

Equilateral Triangle

In an equilateral triangle                                               

  • All the three sides are equal.
  • All the three angles are equal, and each of the angles is equal to 60.
  • Area:   ¾ a2  where a is the side of the equilateral triangle.
  • Height = a 3/2

                                                                       

 a h a                                                                     





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