Euclidean/non-Euclidean geometries in Grade XII

Hi Friends! In this online geometry help session we will discuss geometry and it's types. Geometry is basically classified in two types namely: Euclidean and Non-Euclidean geometries. Euclidean Geometry refers to a high school geometry that deals with straight lines, planes and points, whereas non Euclidian geometry deals with non straight lines which are nothing but curved lines. Euclidean geometries and Non Euclidean geometries are the opposite forms of mathematical geometrical methods in geometry. Euclidean/non-Euclidean geometries in grade XII consists of the understanding and application of many forms of geometrical constructions. The term Euclidean geometry is named after its invention by an ancient Greek mathematician-Euclid (300 BC).Euclidean geometry mainly consists of any two straight lines which follow a path parallel to each other.(parallel means lines which face each other and flow constantly and  remain at an equal distance from each other even if they are extended to any point, parallel lines never intersect each other.)Non Euclidean geometry is of many types which consist of curved lines and the lines may flow in a perpendicular direction with respect to each other. Examples for non Euclidean geometrical diagrams are elliptical forms, hyperbolas etc. The latest or the modern forms of Euclidean's theory are of four types which are most commonly used and known. They are the Pythagoras theorem, Thales theorem, Bridge of asses theorem and sum of angles theorem which states that the sum of all the angles of any triangle is always equal to 180 Degrees. Simple examples of Euclidean geometry are squares, rectangles, quadrilaterals. A parallelogram is another example that has two sides parallel to each other and are measured and drawn using scales, where as Non Euclidean Geometrical examples include spherical shapes, elliptical shapes, which are in the form of a curve.
HYPERBOLA is a practical Example for Non euclidean geometrical (for more see this)form which consists of the line that touches the x axis and passes through the y axis.It meets all the criteria of a non euclidean geometrtical form like being in curved way,or non striaght form that cannot be drawn using a scale.

Here  we have a wonderful example for euclidean geometry, which consists of parallel lines in the rectangle (also see What is the Area of a Rectangle)given.in the next topic we are going to discuss formal and informal proofs.
In the next topic we are going to discuss Formal/informal proofs

In upcoming posts we will discuss about Formal/informal proofs and variance of discrete random variable. Visit our website for information on Maharashtra state board books