# Geometrical Propositions Tutorial

A subdivision of mathematics that deals with properties of shape, curves and surfaces usually separated into two types, Arithmetical and geometry in consent with the mathematical techniques. The association between Algebra and geometry was introduced by Descartes. He introduces fundamental algebraic entity ‘number’ to the fundamental geometrical concepts of ‘point’. This association is call as ‘system of co-ordinates’. The geometry has classified into three types. These are plane geometry, solid geometry, and spherical geometry.

## Basic geometrical propositions tutorial concepts

Point: It has an approximate position is called as point

Line: Connect two points and extend in both directions. Characterize the ends using arrow-heads on either side

Ray: Ray starts from a stable point and extends constantly in single direction.

Line segment: A line segment is a division of a line containing two end points on it.

Plane: A plane is a flat surface which extends continuously in every one direction. A division of a plane can be drawn on any flat surface.

Perpendicular: If the two lines interconnect at accurate angles, then the two lines are called perpendicular to each other.

## Example problems of geometrical propositions tutorial

Ex 1:

How do you find the slope of the geometrical propositions tutorial line at the following points (20, 10) and (25, 10).

Sol:

Take (20, 5) as (x1, y1) and (25, 10) as (x2, y2)

Then, the slope of the line = (y2-y1) / (x2-x1)

m = (10-5) / (25-20)

On solving this, we obtain

m= 5/5

m= 1.

Ex 2:

If 3x + 5y = 10 and 2x + 3y = 5 then find the value of x and y of the geometrical propositions tutorial?

Sol:

Here given two equations, solving the two equations and find the value of x and y

(1) *2 =        6x + 10y = 20

(2) * 3 =       6x + 9y = 15
(-)    (-)    (-)

y = 5

On solving this, We get

y = 5

Substitute y =5 in (1) equation

3x + 5(5) = 10

x = -5.