PRE-GEOMETRY

“Thinking about thinking”

BASIC CONCEPTS

Geometry is being defined as visual mathematics.

Geometry of today was written down and discovered in ancient time guys like Pythagoras and Euclid.

Actually today's geometry in schools is known Euclidian geometry.

Points, lines, planes and space are building blocks of geometry.

We are going to see a lot of different shapes and how they are put together then we take a look relationships between one shape and another.

Basic concepts

In geometry, it doesn’t get basic much more then point.

Point: point is a dot which has no length, width, and thickness. It is just a place holder. We use capital letters to represent points such as A, B, X, W, ….

Basic concepts

Line: a line is a straight arrangement of points. Line has no width and thickness but its length extends infinity in two directions. Usually we name lines with lower case italic letters such as l, d, m, n, … or by naming two points and topping them with two-arrow symbol.

Basic concepts

l

.. BA

AB

Intersecting lines: two lines those have at least one common point are called intersecting lines. Common point is called intersection point.

Basic concepts

l

m

Parallel lines: two coplanar lines those don’t have any intersection (common point) are called parallel lines. We denote parallelism with symbol of ||

Basic concepts

l

m

m || l

Coincident lines: two lines are coincident if each one contains all the points of the other one.

Basic concepts

lm

Collinear points: points which lie on the same line are called collinear points.

Basic concepts

.BA. . .C D

Ray: a ray lies like a line except begins from one point and extends in one direction to infinity. Just like rays of the sun. We denote ray using single arrow at the top of points.

Basic concepts

BA.

.AB

Segment (line segment): a segment is a part of a line between two different points. We denote segment with a solid line at the top of points.

Basic concepts

BA. .AB

A ray has one end point,A segment has two end points,A line has no end points.

Basic concepts

Plane: think about a flat surface area like a table which extends infinitely in all directions is called a plane. A plane has length and width but no thickness. We denote plane with ( ). Example: (P), (O), (R),….

Basic concepts

P

Coplanar points: points on the same plane are called coplanar points.

Basic concepts

P . ... .A

BC

ED

Coplanar lines: lines on the same plane are called coplanar lines.

Basic concepts

P

Skew lines: two lines those non-coplanar and not intersecting are called skew lines.

Basic concepts

lm

Space: set of all points is called space. Points, lines, planes are all somewhere in space.

Basic concepts

Angles

Angle: an angle is two rays or segments those share the same endpoint.

Interior and exterior region:

The region between the sides and contains angle is called interior region.

The region which doesn’t contain angle is called exterior region.

Measuring angles:

One unit of measurement of an angle is the degree. It is 1/360 of a full revolution.

We can use a protractor to measure angles in degrees.

Protractor: circular protractor

Protractor: semi-circular protractor

How to measure an angle using protractor?

place the centre of the protractor on the vertex of the angle

match the 0° horizontal centre line with one of the arms of the angle

read the size of the angle, indicated by the other arm.

60°

How to construct an angle using protractor? Draw a straight line. Put a dot at one end of the line. (The line

represents one of the arms and the dot represents the vertex of the angle.) Place the protractor so that its centre is on the vertex and 0° is on the baseline.

Find the required angle on the scale and mark a small dot at the edge of the protractor.

Join the small dot with the vertex to form the second arm of the angle.

Label the angle.

130°

Types of angles

Angles can be classified according to their size.

Acute angle: An angle measures bigger than 0° less than 90° is called acute angle.

Types of angles

Right angle: A right angle is an angle that equals exactly 90°.

Types of angles

Obtuse angle: An obtuse angle is greater than 90° but less than 180°.

Types of angles

Straight angle: A straight angle equals exactly 180°.

Types of angles

Reflex angle: A reflex angle is greater than 180° but less than 360°.

Types of angles

Revolution or Complete angle: A revolution, or a complete is an angle of 360° (a full circle).