A Presentation by Green House :

Finola- xii (b)Judson Jude- xi (b)suriyamanivasagan- xii (a)

GEOMETRIC BONANZA

WHAT IS GEOMETRY ? The branch of mathematics concerned with the properties

and relations of points, lines, surfaces, solids, and higher dimensional analogues.

What is GEOMETRIC BONANZA ?Geometric Bonanza refers to a sudden increase or a growth in the field

of Geometry.

What made the sudden increase or How did Geometry grow?This is made possible by the use of Geometry in our

daily life.

The History of GeometryGeometry's origins go back to approximately 3,000 BC in ancient Egypt. Ancient Egyptians used an early stage of geometry in several ways, including the surveying of land, construction of pyramids, and astronomy. Around 2,900 BC, ancient Egyptians began using their knowledge to construct pyramids with four triangular faces and a square base.

Euclid's Elements

The next great advancement in geometry came from Euclid in 300 BC when he wrote a text titled 'Elements.' In this text, Euclid presented an ideal axiomatic form (now known as Euclidean geometry) in which propositions could be proven through a small set of statements that are accepted as true. In fact, Euclid was able to derive a great portion of planar geometry from just the first five postulates in 'Elements.'

These postulates are listed below: (1) A straight line segment can be drawn joining any

two points. (2) A straight line segment can be drawn joining any

two points. (3) Given any straight line segment, a circle can be

drawn having the segment as radius and one endpoint as center.

(4) All right angles are congruent. (5) If two lines are drawn which intersect a third line

in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended infinitely.

Euclid's fifth postulate is also known as the parallel postulate.

Plane Geometry Point Line Ray Plane Parallel lines Intersecting lines Perpendicular lines Angles

PointA point is an exact position or location on a plane surface. It is important to understand that a point is not a thing, but a place. An exact location in space.

LineAn endless collection of points along a straight path. The equation of line is : y = mx+c

RayPart of a line that has one endpoint and extends endlessly in the other direction. Any of a set of straight lines passing through one point.

PlaneA plane is a flat, two dimensional surfaces that extends infinitely far. An endless, flat surface that is named by any three points not on the same line.A plane is the two- dimensional analogues of a point (zero dimensions), a line (one dimension) and three-dimensional space.

Parallel Lines

Two different lines do not intersect but are in the same plane.

Intersecting Lines

Two or more lines that meet at a point are called intersecting lines. The point where intersecting lines meet is called the point of intersection. There is no limit to the number of lines that can share a point of intersection.

Perpendicular Lines Perpendicular is the relationship between two lines which meet at a right angle (90 degrees).

AnglesAn angle is formed when two rays have the same endpoint. This endpoint is called the vertex.The two rays that form the angle are called sides.

There are six types of angles, the important four are ; Right angle Straight angle Acute angle Obtuse angle

Right AngleA right angle is an angle that bisects the angle formed by two adjacent parts of a straight line.

Straight Angles An angle whose measure is exactly 180° - a straight line.

Acute AngleThe acute angle is the small angle which is less than 90°.

Obtuse AngleThe obtuse angle is the smaller angle. It is more than 90° and less than 180°. The smaller angle is an Obtuse Angle, but the larger angle is a Reflex Angle.

Quadrilateral

A quadrilateral is a polygon with four edges (or sides) andfour vertices or corners.

Polygons

A closed plane figure made up of several line segments that are joined together. The sides do not cross each other. 

Symmetry

If there is a line going through it which divides it into two pieces which are mirror images of each other.

Pythagoras Theorem

The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

Solid Geometry

• Solid Geometry is the geometry of three-dimensional space - the kind of space we live in ...

• ... let us start with some of the simplest shapes:

Polyhedra and Non-Polyhedra

POLYHEDRA -Shapes having flat faces. E.g.:

NON- POLYHEDRA

Shapes having surfaces that are not flat. E.g;

GEOMETRY IN EVERYDAY

LIFE

PERPENDICULAR LINES

This is part of wall in any construction is assumed as perpendicular lines.

This is part of the fence of the tennis court. The posts are parallel.

Intersecting Lines Part of the

gate has lines that are intersecting. In this case, the line in the middle is a support for the vertical lines.

Polygon• The white “stop” strip in the parking lot is an example of a rectangle.

PolygonThe American Flag is a great example of several polygons. In this case, each stripe is a rectangle along with the blue. The stars are polygons as well which are convex.

3-Dimensional Shapes

The podium is an example of a trapezoidal prism.

*The trash can is an example of a rectangular prism.

Let us have a look at some of the Real life geometric shapes in this video.