## GEOMETRY - ESSENTIAL POINTS

• The point denotes a certain position at fixed place.
• Line: A line is perfectly straight and extends forever in both directions.
• Line segment: A line segment is the part of a line between two points.
• Ray: A ray is part of a line that starts at one point and extends forever in one direction.
• A line-segment has two end points.
• A ray has only one end point (its vertex).
• A line has no end points on either side.
• Intersecting lines: Two or more lines that have one point in common.
• When two lines a and b intersect; the point of their meet is called the point of intersection. These lines are intersecting because they meet or cut at the point P.

• Parallel Lines: When 2 lines do not meet at any point however far we extend them, we call these lines as parallel lines.

The line AB and the line CD are parallel, because even if both the lines are extended left or right they would not meet. The lines EF and GH are parallel, because even if these lines are extended at top or bottom, they would not meet.
• An infinite number of lines can be drawn to pass through a given point.
• One and only one line can be drawn to pass through the given points A and B.
• Concurrent Lines: Three or more lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point.
• The curves that start and end at the same point are called Closed figures.
• A closed figure which does not intersect itself is called a simple closed figure.
• A simple close figure formed of three or more lines is called a Polygon.
• Types of Polygons
• A Polygon with 3 sides : Triangle
• A Polygon with 4 sides : Quadrilateral
• A Polygon with 5 sides : Pentagon
• A Polygon with 6 sides : Hexagon
• A Polygon with 7 sides : Heptagon
• A Polygon with 8 sides : Octagon
• A Polygon with 9 sides : Nonagon
• A Polygon with 10 sides : Decagon
• A polygon is made of line segments.
• A triangle is a polygon with three sides.
• A triangle has three sides, three vertices, and three angles.
• The three internal angles of a triangle always add upto 180 degrees.
• An equilateral triangle has three sides of equal length and three equal angles.
• An isosceles triangle has two sides of equal length and two equal angles.
• A scalene triangle has no sides of equal length and no equal angles.
• A right angle triangle has one angle that is 90 degrees.
• An obtuse triangle has one angle larger than 90 degrees and two acute angles.
• An acute triangle has all the three angles less than 90 degrees.
• A circle is a closed figure each of whose points is equidistant from a fixed point inside it, called the centre.
• A circle is a shape which has no sides.
• The distance between the centre point of the circle and any point on its circumference is called the radius.
• The line segment the joins two points on a circle is called its chord.
• Diameter is the longest chord in a circle.
• The length of the boundary of a circle is called the circumference of the circle.
• The quadrilateral is a polygon with 4 sides.
• A line segment joining the opposite vertices of a quadrilateral are called its Diagonals.
• A Rectangle is a special type of quadrilateral in which its opposite sides and diagonals are equal.
• A Square is a special type of rectnagle in which all sides are equal.