Equilateral Triangle

Author:
DSt1017

What is an equilateral triangle?

Check all that apply
We are now going to see how to make an equilateral triangle with just a ruler and compass
Open the compass tools drop down menu, and choose "Circle with Center through Point". Click on one of the dots at either end of the line. This will be the centre of the circle you are about to draw. Next, click on the other dot. The distance between your two clicks will be the radius and Geogebra will draw the circle all the way round for you. Then, draw another circle of the same radius (the distance between A and B) but with the other dot as the centre. There is an undo and a restart button if you get stuck.
Zoom out a bit (scroll down on your mouse) and you will hopefully have something looking like the above.

Look at where the two circles intersect (where the curves cross over each other at C and D). Which of the following is true for point C?

Check all that apply
We also know that Point C is the same distance from Point A as Point B is from A as they are both on the circle with centre A. Therefore we have three points the same distance away from each other and can join them up to get our special equilateral triangle. Have a go now with the applet at the top of the page. To finish, you can right click your construction lines to hide them. Well done!

Bonus question!

We know that there are in a triangle. By symmetry we can see that all the angles in our equilateral triangle are equal. What is the size of each angle, in degrees?