Incenter Investigation

Euler Line Investigation


In this section of the exploration you will be asked to discover the amazing property that certain points of concurrency are collinear, i.e. lie on the same line, independent of the configuration of the triangle. Your investigation will result in a discovery, known long ago before people could use computers. This discovery was named after Euler, a great mathematician and scientist, whose profound work and genius have greatly influenced the development of our understanding of the world. Thus using the power of modern technology, you will be able to understand properties that have puzzled some of the greatest minds of the past. So, try hard and patiently and you will be rewarded with intriguing discoveries. As you work through the material, you may be asked to write down the answers to the questions in the investigation or to save the information and your sketch on a disk.

We start our journey with our old friend -- the triangle. There is nothing simpler than a triangle, just three points and segments that connect them, but what a world of unexpected relations! You have already been introduced to some of them -- the four points of concurrency. Could you name them? If you have doubts about the names of the points and their definitions, check here.


We are not done yet. We still have properties to discover. Follow the directions ahead.

Now you can relax. You have discovered some of the properties of the Euler's line. You will discover more properties when you investigate the nine point circle.

Do you know that mathematician do not stop here? This is just the beginning of another world, where mathematicians enter with conjectures and come out with a proof! Conjectures are not always true! You have to prove them with logic and serious argument. To do so you need to know the rules, be very persistent and study a lot more mathematics... This is what mathematicians do!

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