1. Results on Triangles:
- Sum of the angles of a triangle is 180°.
- The sum of any two sides of a triangle is greater than the third side.
- Pythagoras Theorem:In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2.
- The line joining the mid-point of a side of a triangle to the positive vertex is called the median.
- 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.
- In an isosceles triangle, the altitude from the vertex bisects the base.
- The median of a triangle divides it into two triangles of the same area.
- 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:
- The diagonals of a parallelogram bisect each other.
- Each diagonal of a parallelogram divides it into triangles of the same area.
- The diagonals of a rectangle are equal and bisect each other.
- The diagonals of a square are equal and bisect each other at right angles.
- The diagonals of a rhombus are unequal and bisect each other at right angles.
- A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
- Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area.
I. 1. Area of a rectangle = (Length x Breadth).
Length = and Breadth =
2. Perimeter of a rectangle = 2(Length + Breadth).
II. Area of a square = (side)2 = (diagonal)2.
III. Area of 4 walls of a room = 2 (Length + Breadth) x Height.
IV. 1. Area of a triangle = x Base x Height.
2. Area of a triangle =
where a, b, c are the sides of the triangle and s = (a + b + c).
3. Area of an equilateral triangle = x(side)²
4. Radius of in circle of an equilateral triangle of side a =
5. Radius of circumcircle of an equilateral triangle of side a =
6. Radius of incircle of a triangle of area and semi-perimeter s =
V. 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.
VI. 1. Area of a circle = R² , where R is the radius.
2. Circumference of a circle = 2R.
3. Length of an arc = where is the central angle.
4. Area of a sector = (arc x R)=
VII. 1. Circumference of a semi-circle = R.
2. Area of semi-circle =