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List Of All Chapters On Lines, Angles And Shapes

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Introduction

In the fundamentals of geometry, the point, line, ray, angle and the shapes like circle, triangles and quadrilaterals are studied. It has been in use and keeps on evolving with time from 3000 BC to today's geometry.

The early geometry was used by ancient Babylonia and Indus Valley civilizations around 3000 BC. They used geometry in astronomy by plotting the daily speed and distance travelled by the planet Jupiter. Thales of Miletus used geometry in calculating the height of the Great Pyramid in Egypt.

Pythagoras who was a Greek philosopher and polymath made contributions to geometry with his famous Pythagorean Theorem. Later Euclid made influential contributions which he documented in the book Elements consisting of 13 volumes around 300 BC. The book covers the topics of plane geometry, solid geometry, flat surfaces and conic sections.

Archimedes, the Greek mathematician in the period of 287 BC to 212 BC, worked in Geometry by proving many theorems, some of them are to find area under arc of parabola and area of a spiral.

Aryabhata, an Indian mathematician and astronomer in 476 to 550 CE, made important contributions such as in calculating the accurate value of pi constant (π).

René Descartes, in the 17th century, developed a cartesian coordinate geometry system which is used to locate a point in a two dimensional space.

Fundamentals of Geometry lessons

GEOMETRY > FUNDAMENTALS OF GEOMETRY

Point, Line, Ray, and Plane In Geometry

Definitions of point, line, ray, line segment, and the plane in geometry. Learn to name the different types of lines in free worksheets.
Table of contents
  • Point
  • Line
  • Ray
  • Line segment
  • Plane in geometry
  • Intersecting lines
  • Perpendicular lines
  • Parallel lines
  • Transversal line
  • Concurrent lines
  • What are collinear points?
Rupinder Kaur
Aug 18, 2026
2D Shapes Coordinate Geometry Lines
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Angles And Its Types Based On Its Different Measures

Start with the definition of an angle, its different types & measures. Learn congruent, complementary, and supplementary angles with diagrams.
Table of contents
  • What is an Angle?
  • Measurement of angle
  • Types of angle
  • What are congruent angles?
  • What are adjacent angles?
  • List of types of angles with measures
Rupinder Kaur
Aug 18, 2026
Angles
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Angles Made On Parallel Lines By Intersecting Line

Which angles are created by a transversal on parallel lines? Learn when alternate and corresponding angles are equal. Solve questions of missing angles.
Table of contents
  • Exterior angles
  • Interior angles
  • Transversal crosses parallel lines
  • Alternate angles
  • Corresponding angles
  • Vertically opposite angles
Rupinder Kaur
Aug 18, 2026
Angles Lines
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Triangle And Its Types Based On Size Of Sides And Angles

Start with learning the sides, vertex, and angles of a triangle. Know the different types based on the length of its sides and size of angles.
Table of contents
  • Definition
  • Number of sides
  • Vertices
  • Angles
  • Types based on sides length
  • Types based on size of angles
Rupinder Kaur
Aug 18, 2026
2D Shapes Angles
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Area And Perimeter Of Different Types Of Triangle

Learn formulas and practice how to calculate area and perimeter of isosceles and equilateral triangles with solved examples and free worksheets.
Table of contents
  • Perimeter
    • Triangle
    • Equilateral triangle
    • Isosceles triangle
  • Area
    • Area of triangle
    • Area of equilateral triangle
    • Area of isosceles triangle
Rupinder Kaur
Jul 18, 2026
2D Shapes Area Perimeter
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Polygon's Types And Classification Based On Sides

Start learning with vertices, angles & sides of polygon. Know the types like convex, concave, pentagon, hexagon etc. Practice problems to find the angles.
Table of contents
  • Curve
  • Polygon
    • Adjacent sides
    • Adjacent vertices
    • Diagonals
  • Types of polygon
    • Convex polygon
    • Concave polygon
    • Regular polygon
    • Irregular polygon
    • Simple polygon
  • Types based on number of sides
Rupinder Kaur
Aug 18, 2026
2D Shapes
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Quadrilateral's Sides, Diagonals And Its Types

Learn the definitions of different types of quadrilateral like a parallelogram, rectangle, rhombus, & more. What are their diagonals and adjacent sides?
Table of contents
  • Quadrilateral
    • Adjacent sides
    • Opposite sides
    • Diagonals
  • Types of quadrilateral
    • Parallelogram
    • Rectangle
    • Square
    • Rhombus
    • Trapezium
  • Shape of isosceles Trapezium
  • Shape of kite
Rupinder Kaur
Aug 18, 2026
2D Shapes
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Area And Perimeter Of Parallelogram, Rectangle, Rhombus And Trapezium

Learn formulas and calculations of area and perimeter of quadrilaterals like parallelogram, rectangle, square, rhombus and trapezium.
Table of contents
  • Perimeter of quadrilateral
  • Area of quadrilateral
  • Perimeter of parallelogram
  • Area of parallelogram
  • Perimeter of rectangle
  • Area of rectangle
  • Perimeter of square
  • Area of square
  • Perimeter of rhombus
  • Area of rhombus
  • Area and perimeter of rhombus with diagonals
  • Perimeter of trapezium
  • Area of trapezium
Rupinder Kaur
Aug 18, 2026
2D Shapes Area Perimeter
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Circle's Radius, Diameter, Chord And Tangent

What is a circle? Know about its diameter, arc, secant, sectors and segments. Practice questions on recognizing its parts by solving free worksheets.
Table of contents
  • Center and radius
  • Diameter
  • Chord
  • Secant
  • Tangent
  • Arcs of circle
  • Sectors of circle
  • Segments of circle
  • Semi circle
Rupinder Kaur
Jul 14, 2026
2D Shapes
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Circle's Circumference And Area Of Sectors And Segments

Learn how to calculate the area & circumference of a circle. Refer the list of formulas to find areas of the sector, segment, semicircle & length of arc.
Table of contents
  • Circle
  • Semi circle
  • Area of minor sector
  • Area of major sector
  • Area of minor segment
  • Area of major segment
  • Length of arc
  • Formulas list of areas & perimeters
Rupinder Kaur
Aug 18, 2026
2D Shapes Area Perimeter
GEOMETRY > FUNDAMENTALS OF GEOMETRY

Cartesian Coordinate System And Quadrants

How are x and y axes scaled in the Cartesian coordinate system with sign conventions? Learn how to locate the coordinates of a point in quadrants.
Table of contents
  • x and y coordinate axes
  • Positive and negative directions of axes
  • How to scale x and y axes?
  • What are the four quadrants?
  • Locate coordinates of a point
  • Sign conventions used in quadrants
Rupinder Kaur
Aug 18, 2026
Coordinate Geometry Lines
Geometry
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