What is a geometric construction?

When it comes to geometry, the term constructions is basically used in order to denote the drawing of lines, shapes and angles in a very accurate manner. However, the one thing that you need to know about geometric constructions is that these can be made using merely a ruler or straightedge, a compass and a pencil. If truth be told, these are the purest forms of geometry constructions considering that they do not have any numbers involved at all. Moreover, the one thing that you need to bear in mind about these is that it isn’t allowed for you to measure any lengths within these with the help of a ruler, or measure angles with the help of a protractor.

Information about basic geometric constructions

Every single straightedge and compass based construction out there is based upon the continual application of five basic geometric constructions that make use of lines, circles and points which have been constructed already. The basic geometric constructions are inclusive of:

  • Taking two existing points and creating a line through them
  • Taking two points and creating a circle through them
  • Taking two non-parallel, already existing lines and creating their intersection point
  • Taking two circles and creating their intersection points in case they intersect
  • Taking a line and a circle and a line and creating their intersection points in case they intersect

Consider an example. Suppose we have two distinct points at hand, it allows us to create a line through them or even two circles. Now if two circles are drawn, then their intersection allows us to formulate two new points. If you draw lines amid the two original point along with one of the two newly created points, then this is going to help you construct an equilateral triangle.

A look into the history of geometric constructions

Looking back in time, we are sure to realize that the Greeks played a major part in the formulation of much of modern geometry. In terms of a geometric construction, it was the famous mathematician Euclid who documented these in his famous book known as ‘Elements’. The history of geometric constructions tells us that in his book, he made extensive utilization of construction techniques. The book also provides information about the concepts of geometry and entails details regarding drawing things wherein direct measurements are not required.

Ian Roberts
San Francisco, USA

"If you're at school or you just deal with mathematics, you need to use Studygeek.org. This thing is really helpful."
Lisa Jordan
Math Teacher
New-York, USA

"I will recommend Studygeek to students, who have some chalenges in mathematics. This Site has bunch of great lessons and examples. "
John Maloney
Student, Designer
Philadelphia, USA

" I'm a geek, and I love this website. It really helped me during my math classes. Check it out) "
Steve Karpesky
Vancuver, Canada

"I use Studygeek.org a lot on a daily basis, helping my son with his geometry classes. Also, it has very cool math solver, which makes study process pretty fun"