Introduction to Geometry

Introduction to Geometry

Last Updated on Oct 14, 2019

The introduction to geometry provides a brief overview of different geometrical shapes. Understanding this topic well is necessary to solve questions that are asked in various competitive exams in the Quantitative Aptitude or Quant section - applicable to CAT, XAT, MAT, SNAP, IIFT, CLAT, AILET, DU LLB, any other entrance exam as well. For more such content, visit our website - examvictor.com

Geometry is that part of mathematics that treats the properties of points, lines, surfaces and solids. Geometry comes from the Greek meaning ‘earth measurement’ and is the visual study of shapes, sizes and patterns, and how they fit together in place.

Point, Line, Plane and Solid

  • A Point has no dimensions, only position
  • A Line is one-dimensional.

    Types of lines :
    Parallel lines never meet or intersect. They simply go on forever side by side, a bit like railway lines.
    Perpendicular lines intersect at a right angle, 90°

  • A Plane is two dimensional (2D)
  • A Solid is three-dimensional (3D)

Plane Geometry
Plane Geometry is all about shapes on a flat surface (like on an endless piece of paper).

Using Drafting Tools

  • Geometric Constructions
  • Using the Protractor
  • Using the Drafting Triangle and Ruler
  • Using a Ruler and Compass
Signs, Symbols and Terminology related to Geometry

Degrees ° a measure of rotation - the angle between the sides.

Angles are commonly marked in geometry using a segment of a circle (an arc), unless they are a right angle when they are ‘squared-off’.

Tick marks indicate sides of a shape that have equal length (sides of a shape that are congruent or that match). The single lines show that the two vertical lines are the same length while the double lines show that the two diagonal lines are the same length. Tick marks can also be called ‘hatch marks’.

A vertex is a point where lines meet (lines are also referred to as rays or edges). The plural of vertex is vertices.

The angle symbol ‘∠’ is used as a shorthand symbol in geometry when describing an angle. The expression ∠ABC is shorthand to describe the angle between points A and C at point B. The middle letter in such expressions is always the vertex of the angle you are describing - the order of the sides is not important. ∠ABC is the same as ∠CBA, and both describe the vertex B.

If you want to write the measured angle at point B in shorthand then you would use:

m∠ABC = 130° (m simply means 'measure')

or

m∠CBA = 130°

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