Chapter 4 - Basic Geometrical Ideas

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Introduction to Geometric Shapes

The term 'Geometry' comes from the Greek word Geometron. Geo means Earth and metron means Measurement. Geometrical ideas are reflected in all forms of art, measurements, architecture, engineering, and designing.

Starting from basic objects like tables and books to the world-famous monuments, everything can be defined in terms of their geometrical shapes.

Famous Monuments and their Shapes

The Great Pyramid of Giza is well known for its distinct shape. All the faces of the pyramid are triangular in shape and its base is a square.

The Taj Mahal has a square base, a circular dome, and four cylindrical minarets.

The Leaning Tower of Pisa has a circular base and a cylindrical body.

It's not only the famous monuments, we can use geometrical shapes to define even the simplest of objects like books, tables, and bottles.

Points, Line Segments, Rays and Lines

Geometrical shapes like squares and triangles are made up of basic units like points, lines, rays, and angles.

Point

Take a sharp pencil and mark a dot on a piece of paper. The dot is invisibly thin. This tiny dot is called a point.

We use points on a geometrical shape to mark specific positions. When we use several points together, we name them as A, B, C, D etc. for easy recognition.

Line Segment

We join two points together to get a line segment. The line segment ${AB}↖{−}$ connects the points A and B.

Line

If the line segment is extended beyond A in one direction and beyond B in the other direction without any end, then we get a line. The line is denoted as ${AB}↖{↔}$.

Intersecting lines and parallel lines

When two lines meet at some point we call them as intersecting lines and their meeting point is called as intersecting point.

When two lines never intersect, they are known as parallel lines.

Ray

A ray is a portion of line which starts at a point on the line and goes endlessly in a particular direction.

The ray ${AB}↖{→}$ starts from A and goes towards B and moves beyond it.

Geometrically, a ray has a starting point and no ending point. When a torch light or a bulb is glowing, we get light rays. We get light rays from the Sun as well.

Curves and Polygons

Curve can be defined as the continuous movement of points in any direction. So, all possible shapes can be classified as curves because all are formed by the movement of points in single or multi-dimension.

A necklace, a snake, and a slack rope are a few examples of curved figures.

In general, a curve is an entity that is not straight but in mathematics, even a straight line is a curve.

Types of Curves

• Some curves do not cross themselves. These are called simple curves.
• Curves that do not have any opening are called closed curves.
• Curves that do not close a path are called open curves.

Polygons

Mathematically, polygons are two-dimensional closed figures that are entirely made up of line segments. The line segments that complete the polygon are known as sides of the polygon.

The common points where two sides meet are known as the vertices (vertex as singular). The number of vertices in a polygon is equal to its number of sides.