Geometry has a long and rich history. The term ‘Geometry’ is the English equivalent of the greek word ‘Geometron’.
The meaning of geometry includes:
 Geo means Earth
 metron means Measurement.
Therefore, geometry refers a branch of Mathematics that studies the sizes, shapes, positions angles and dimensions of things.
It is used to calculate the area or capacity related to any shape.
Line Segment
Joining two points A and B is denoted by \(\overline{\mathrm{AB}}\) or \(\overline{\mathrm{BA}}\).
The points A and B are called the endpoints of the segment.
Intersecting lines
The two lines that share one common point.
This shared point is called the point of intersection.
Here, line l and m are intersecting at point C.
Parallel Lines
Two or more lines that never intersect or Never cross each other are called Parallel Lines.
Ray
It is a part of a line with one starting point whereas extends endlessly in one direction.
Curves
Anything which is not
straight is called a curve.
1. Simple Curve:
A curve that does not cross itself.
2. Open Curve:
Curve in which its endpoints do not meet.
3. Closed Curve:
Curve that does not have an endpoint and is an enclosed figure.
Parts of Curve
A closed curve has 3 parts which are as follows:
1. Interior
2. Exterior
3. Boundary
1. Interior of the curve
 It refers to the inner area of the curve.
 The blue coloured area is the interior of the figure.
2. The exterior of the curve.
 It refers to the outer area of the curve.
 The point marked A depicts the exterior of the curve.
3. The boundary of the curve
 It refers to the dividing line thus it divides the interior and exterior of the curve.
 The black line which is dividing the interior and exterior of the curve is the boundary.
 The interior and boundary of the curve together are called the curves “region”.
Polygon
A closed curve made up entirely of line segments.
It is a 2d closed shape made of line segments / straight lines only.
Parts of a Polygon
Sides
 It refers to the line segments which form the polygon, as in the above figure AB, BC, CD, DA are its sides.
Vertex
 Point where 2 line segments meet, as in the above figure A, B, C and D are its vertices.
Adjacent Sides

If any 2 sides share a
common endpoint they are said to be adjacent to each other thus called adjacent
sides.
 As in the above figure AB and BC, BC and CD, CD and DA, DA and AB are adjacent sides.
Adjacent Vertices

It refers to the endpoints
of the same side of the polygon.
 As in the above figure A and B, B and C, C and D, D and A are adjacent vertices.
Diagonals

It refers to the joins of
the vertices which are not adjacent to each other.
 As in the above figure, AC and BD are diagonals of the polygon.
Angles
 It’s made up of two rays starting from a common endpoint.
Angles
It’s made up of two rays starting from a common endpoint.
A Below Figure formed from 2 rays which share a common endpoint.
The rays forming the angle are known as its arms or sides.
The common endpoint is known as its vertex.
An angle is also associated with 3 parts:

Interior 
 It refers to the inner area.
 The green coloured area is the interior of the angle.
 Angle/boundary 
 It refers to the arms of the angle.
 The red point is on the arm of the angle.
 Exterior 
 It refers to the outer area.
 The blue point depicts the exterior of the figure.
Naming an Angle:
While naming an angle the letter depicting the vertex appears in the middle.
Example
 The above angle can also be named as ∠CBA.
 An angle can also be named just by its vertex.
Example
Triangle
It is a 3sided polygon. It is also the polygon with the least number of the sides.
 Vertices: A, B and C
 Sides: AB, BC and CA
 Angles: ∠A, ∠B and ∠C
 Here, the light blue coloured area is the interior of the angle.
 The black line is the boundary.
 Whereas, the dark blue area is the exterior of the angle.
Quadilaterals
 It’s a 4sided polygon.
 Vertices: A, B, C, D
 Sides: AB, BC, CD, DA
 Angle: ∠A, ∠B, ∠C, ∠D
 Opposite Sides: AB and DC, BC and AD
 Opposite Angles: ∠B and ∠D, ∠A and ∠C
 Adjacent Angles: ∠A and ∠B, ∠B and ∠C, ∠C and ∠D, ∠D and ∠A.