GEOMETRY FORMULA

• a line of collection of points which can be extended in both direction is called a straight line
• a line segment is a part of a straight line having two end points
• a ray is a part of a line having one endpoint and is endless in the other direction
• an angle is a plain figure formed by two rays having a common end point
• TYPES OF ANGLE

  Acute Angle – an angle measuring less than 90 degrees

  Right Angle – an angle is exactly at 90 degree

  Obtuse Angle – an angle whose measure is greater than 90 degrees and less than 180 degrees

  Straight Angle – an angle which is exactly at 180 degrees

  Reflex Angle – an angle whose measure is greater than 180 degrees and less than 360 degrees

  complete Angle – an angle whose measure is exactly 360 degrees
• if three or more points lie on the same line, it is called a collinear point
• if three or more points does not lie on the same line, the non-collinear point
• two angles having a common arm is called an adjacent angle
• two angles are said to be complimentary if the sum is 90 degree

  two angles are said to be supplementary if the sum is 180 degree
• two adjacent angle whose sum is 180 degree is called a linear pair angle.
• when two lines intersect with eachother, four angles are formed. the pair of angles facing each other are called vertically opposite angle
• if a ray stands on a line, then the sum of two aadacent angles so formed is 180 is called axiom
• theorem 6.1: if two lines intersect each other, then the vertically opposite angles are equal
• theorem 6.6: lines which are parallel to the same line are parallel to eachother
• parallel lines:

  1. a pair of corresponding angles are equal
  2. a pair of alternate angle are equal
  3. a pair of vertically opposite angle are equal
  4. the sum of pair consecutive interior angle is 180 degree
• a triangle is a closed figure bounded by three sides

  1. a triangle has 3 sides
  2. a triangle has 3 angles
  3. a triangle has 3 vertices
  4. the sum of all angles is 180
  5. the sum of 2 sides of a triangle is greater than the third side
• TYPES OF TRIANGLE

  
  

  1. when all the sides are equal, it is called a equilateral triangle
  2. a triangle in which only two sides are equal isis called an isosceles triangle
  3. a triangle in which all sides are different in length are called scalene triangle
• 1. if all the angles of a triangle are equal, it is called an equiangular triangle
  2. if all three angles are less than 90 degrees is it called an acute angle triangle
  3. if one of the angles are 90 degrees, it is called a right angle triangle
  4. if one angle is more than 90 degree, it is called a obtuse angle triangle
• congruence means equal in all respect or figure whose shape and sizes are about the same

  CPCT= corresponding parts of a congruent triangle.
• congruent rule

  side-side-side (SSS),

  side-angle-side (SAS),

  angle-side-angle (ASA),

  angle-angle-side (AAS)

  right angle-hypotenuse-side (RHS).
• area of a circle= πr²
• circumference of a circle= 2πr²
• cureve surface area of a cone= πrl
• slant height= L= √ h²+r²
• total surface area of a cone= πr(l+r)
• surface area of a sphere= 4πr²
• total surface area of a hemisphere= 3πr²
• curved surface of a hemisphere= 2πr²
• volume of a sphere= 4/3πr³
• volume of a sphere= 4/3πr³
• volume of a hemisphere= 2/3πr³
• a quadrilateral is a closed figure bounded by 4 sides
• TYPES OF QUADRILATERAL

  1. parallelogram: a parallelogram is a quadrilateral in which the opposite sides are parallel
  2. rectangle: a rectangle is a quadrilateral in which the opposite sides are parallel and the angle between two adjacent sides is a right angle
  3. square: a square is a quadrilateral in which all four sides are equal and the angle between adjacent sides is a right angle
  4. rhombus: a rhombus is a quadrilateral in which all the four sides are equal
  5. trapezium: trapezium is a quadrilateral in which a pair of opposite sides are equal
• theorem 8.1: a diagonal of a parallelogram divides it into two congruent triangles
• theorem 8.2: in a parallelogram, opposite sides are equal.
• theorem 8.3: each pair of opposite sides equal of a quadrilateral is equal in a parallellogram
• theorem 8.4: in a parallelogram opposite angles are equal
• theorem 8.5: if in a quadrilateral, each pair of opposite angles is equal, then it Is a parallelogram
• theorem 8.6: the diagonals of a parallelogram bisect eachother
• theorem 8.7: the diagonals of the quadrilaterals bisect each other, then it is a parallelogram