It then follows that FLG maintains the same criteria and is an equilateral triangle congruent to FHG. Point H is of equal distance from F as is it from G, and the distance of HF and HG is equal also to the distance of FG. For example, we see that triangle FHG is equilateral. The use of circles of equal radius enables the construction of multiple equilateral triangles that in turn form a hexagon. Using points F, H, J, I, K, L as vertices, construct a hexagon.Ī regular hexagon can be constructed from six congruent equilateral triangles. Mark, each point of intersection amongst each of the three circles. Extend line FG to create a new line FI length 2(FG).Ĭonstruct yet another circle with radius FG and center point, I. Create another circle with radius FG and center point G. Using a compass, draw a circle with radius FG and center F.

$red kite geometry$

Given a line FG, create a hexagon with side length FG. Same height as each other, thus we know that AE and EB are the same lengths which proves that the line we’ve created is indeed a bisector of line AB.Ĭonstruction 2: Creating a hexagon, given a line We know that congruent triangles must have all the same angles and side lengths as each other since both triangles DAC and DBC have two side lengths equal to DB and one shared side length DC, they both have three identical sides to each other and are thus congruent. This demonstrates that the two triangles DAC and DBC are isosceles.īoth triangles also share the same base DC. Because the circles created on points A and B have the same radius, we know that points D and C are an equal distance away from points A and B, thus DB = BC = CA = AD. If we join the points the following way, one sees that we’ve created two isosceles triangles DAC and DBC. The 2 points of intersection of the two circles will be points onīut how can we prove that this line CD is actually a bisector of line AB? One method is to use congruent triangles to show geometrically that CD must be a bisector of AB. From the other point B, create a circle with the same radius this time with B as the center point. Extend the compass to create a circle with a radius a little larger than half of length AB and draw the circle. Our first step is to choose point A as the center point for our compass.

Red kite geometry