Basic Geometry

Basic Geometry

Master fundamental geometry concepts for competitive exams with formulas, theorems, and practice problems.

Important Formulas

Essential geometry formulas to remember

Triangle Area
Area = (1/2) × base × height
Circle Area
Area = πr²
Rectangle Area
Area = length × breadth
Square Area
Area = side²
Circle Circumference
C = 2πr
Pythagoras Theorem
a² + b² = c²
Triangle Angle Sum
∠A + ∠B + ∠C = 180°
Quadrilateral Angle Sum
Sum = 360°

Lines and Angles

Types of lines, angle properties, and angle relationships

Key Topics:

  • Types of Lines (Parallel, Perpendicular, Intersecting)
  • Angle Types (Acute, Obtuse, Right, Straight, Reflex)
  • Angle Relationships (Complementary, Supplementary, Adjacent, Vertical)
  • Angle Properties in Parallel Lines
  • Triangle Angle Sum Property

Important Formulas:

  • Sum of angles in a triangle = 180°
  • Sum of angles in a straight line = 180°
  • Sum of angles around a point = 360°
  • Vertically opposite angles are equal

Triangles

Triangle properties, types, and area calculations

Key Topics:

  • Types of Triangles (Equilateral, Isosceles, Scalene)
  • Triangle Classification by Angles
  • Pythagoras Theorem
  • Congruence and Similarity
  • Median, Altitude, and Angle Bisector

Important Formulas:

  • Area = (1/2) × base × height
  • Perimeter = a + b + c
  • Pythagoras: a² + b² = c² (for right triangle)
  • Area = (abc)/(4R) where R is circumradius

Circles

Circle properties, chords, tangents, and theorems

Key Topics:

  • Parts of a Circle (Radius, Diameter, Chord, Arc, Sector)
  • Circle Theorems (Angle in semicircle, Alternate segment)
  • Tangents and Secants
  • Cyclic Quadrilaterals
  • Inscribed and Circumscribed Circles

Important Formulas:

  • Circumference = 2πr = πd
  • Area = πr²
  • Area of sector = (θ/360°) × πr²
  • Length of arc = (θ/360°) × 2πr
  • Angle in semicircle = 90°

Quadrilaterals

Properties of four-sided polygons

Key Topics:

  • Types of Quadrilaterals (Square, Rectangle, Parallelogram)
  • Rhombus, Trapezoid, and Kite Properties
  • Angle Sum Property
  • Diagonals and Midpoints
  • Area Calculations for Different Types

Important Formulas:

  • Sum of interior angles = 360°
  • Square Area = side², Perimeter = 4 × side
  • Rectangle Area = length × breadth
  • Parallelogram Area = base × height
  • Rhombus Area = (d1 × d2)/2

Polygons

Regular polygons and their properties

Key Topics:

  • Regular vs Irregular Polygons
  • Interior and Exterior Angles
  • Number of Diagonals
  • Area of Regular Polygons
  • Apothem and Circumradius

Important Formulas:

  • Sum of interior angles = (n-2) × 180°
  • Each interior angle = [(n-2)/n] × 180°
  • Number of diagonals = n(n-3)/2
  • Area = (1/2) × perimeter × apothem
  • Exterior angle = 360°/n

Practice Geometry Problems

Test your geometry knowledge with interactive practice questions and step-by-step solutions.

Study Tips

  • Memorize basic formulas and theorems
  • Practice drawing diagrams for problems
  • Understand properties before formulas
  • Use approximation for calculation checks

Free Resources