RESULTS ON TRIANGLE
1.Sum of the angles of a triangle is 180 degrees.
2.The sum of any two sides of a triangle is greater than 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 opposite vertex is called the MEDIAN.
5.The point where the three medians of a triangle meet,
is called CENTROID. The centroid divides 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.
RESULTS ON QUADRILATERALS
1.The diagonals of a Parallelogram bisect each other.
2.Each diagonal of a Parallelogram divides it into two
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 he parallelogram of given sides the parallelogram
which is a rectangle has the greatest area.
FORMULAE
1.Area of a RECTANGLE = length * breadth
Length = (Area/Breadth) and Breadth = (Area/Length)
2.Perimeter of a RECTANGLE = 2(Length + Breadth)
3.Area of a SQUARE = (side)2 = ½ ( Diagonal)2
4.Area of four walls of a room = 2(length + breadth) * height
5.Area of a TRIANGLE = ½ * base * height
6.Area of a TRIANGLE = √[s * (s-a) * (s-b) * (s-c)],
where a,b,c are the sides of the triangle and s = 1/2(a+b+c)
7.Area of EQUILATERAL TRIANGLE = √(3/4)* (side)2
8.Radius of in circle of an EQUILATERAL TRIANGLE of
side a = r / 2√3
9.Radius of circumcircle of an EQUILATERAL TRIANGLE
of side a = r / √3
10.Radius of incircle of a triangle of area ∆ and
semi perimeter S = ∆ / s
11.Area of a PARALLELOGRAM = (base * height)
12.Area of RHOMBUS = 1/2 (product of diagonals)
13.Area of TRAPEZIUM =
=1/2 * (sum of parallel sides)* (distance between them)
14.Area of a CIRCLE =  r2 where r is the radius
15.Circumference of a CIRCLE = 2r
16.Length of an arc = 2 rø / 360, where ø is central angle
17.Area of a SECTOR = ½ (arc * r) = r2ø / 360
18.Area of a SEMICIRCLE = r2 / 2
1.Sum of the angles of a triangle is 180 degrees.
2.The sum of any two sides of a triangle is greater than 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 opposite vertex is called the MEDIAN.
5.The point where the three medians of a triangle meet,
is called CENTROID. The centroid divides 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.
RESULTS ON QUADRILATERALS
1.The diagonals of a Parallelogram bisect each other.
2.Each diagonal of a Parallelogram divides it into two
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 he parallelogram of given sides the parallelogram
which is a rectangle has the greatest area.
FORMULAE
1.Area of a RECTANGLE = length * breadth
Length = (Area/Breadth) and Breadth = (Area/Length)
2.Perimeter of a RECTANGLE = 2(Length + Breadth)
3.Area of a SQUARE = (side)2 = ½ ( Diagonal)2
4.Area of four walls of a room = 2(length + breadth) * height
5.Area of a TRIANGLE = ½ * base * height
6.Area of a TRIANGLE = √[s * (s-a) * (s-b) * (s-c)],
where a,b,c are the sides of the triangle and s = 1/2(a+b+c)
7.Area of EQUILATERAL TRIANGLE = √(3/4)* (side)2
8.Radius of in circle of an EQUILATERAL TRIANGLE of
side a = r / 2√3
9.Radius of circumcircle of an EQUILATERAL TRIANGLE
of side a = r / √3
10.Radius of incircle of a triangle of area ∆ and
semi perimeter S = ∆ / s
11.Area of a PARALLELOGRAM = (base * height)
12.Area of RHOMBUS = 1/2 (product of diagonals)
13.Area of TRAPEZIUM =
=1/2 * (sum of parallel sides)* (distance between them)
14.Area of a CIRCLE =  r2 where r is the radius
15.Circumference of a CIRCLE = 2r
16.Length of an arc = 2 rø / 360, where ø is central angle
17.Area of a SECTOR = ½ (arc * r) = r2ø / 360
18.Area of a SEMICIRCLE = r2 / 2
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