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FUNDAMENTAL CONCEPTS

  1. Results on Triangles:
    1. Sum of the angles of a triangle is 180°.
    2. The sum of any two sides of a triangle is greater than the third side.
    3. Pythagoras Theorem: In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.
    4. The line joining the mid-point of a side of a triangle to the positive vertex is called the median.
    5. The point where the three medians of a triangle meet, is called centroid. The centroid divided each of the medians in the ratio 2 : 1.
    6. In an isosceles triangle, the altitude from the vertex bisects the base.
    7. The median of a triangle divides it into two triangles of the same area.
    8. The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle.
  2. Results on Quadrilaterals:
    1. The diagonals of a parallelogram bisect each other.
    2. Each diagonal of a parallelogram divides it into triangles of the same area.
    3. The diagonals of a rectangle are equal and bisect each other.
    4. The diagonals of a square are equal and bisect each other at right angles.
    5. The diagonals of a rhombus are unequal and bisect each other at right angles.
    6. A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
    7. Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.

IMPORTANT FORMULAE

  1. 1.   Area of a rectangle = (Length x Breadth).
          Length =Areaand Breadth =Area.
    BreadthLength
    2.   Perimeter of a rectangle = 2(Length + Breadth).
  2. Area of a square = (side)2 = (diagonal)2.
  3. Area of 4 walls of a room = 2 (Length + Breadth) x Height.
    1.  Area of a triangle = x Base x Height.  
    2.  Area of a triangle = s(s-a)(s-b)(s-c)
            where a, b, c are the sides of the triangle and s = (a + b + c).
      3.   Area of an equilateral triangle =3x (side)2.
      4
      4.   Radius of incircle of an equilateral triangle of side a =a.
      23
      5.   Radius of circumcircle of an equilateral triangle of side a =a.
      3
      6.   Radius of incircle of a triangle of area and semi-perimeter r =.
      s
  5. 1.   Area of parallelogram = (Base x Height). 2.   Area of a rhombus = x (Product of diagonals). 3.   Area of a trapezium = x (sum of parallel sides) x distance between them.
  6. 1.   Area of a circle = R2, where R is the radius. 2.   Circumference of a circle = 2R.
    3.   Length of an arc =2R, where is the central angle.
    360
    4.   Area of a sector =1(arc x R)=R2.
    2360
  7. 1.   Circumference of a semi-circle = R.
    2.   Area of semi-circle =R2.
    2