College Geometry: Construct an equilateral triangle

Equilateral Triangle

I°) Definition of equilateral triangle

I.1°) Definition:

An equilateral triangle is a triangle whose three sides are of equal length (or isometric).

I.2°) Construct an equilateral triangle:

Let [AB] any segment. We successively trace the circle with center A and radius AB and the circle of center B and radius AB. Let C be the intersection of these two circles.

The triangle ABC is equilateral then.

We have: AB = AC = BC.
The three angles are equal.

II°) Properties of equilateral triangle

In an equilateral triangle, the angles are equal and measure 60 degrees.	Re-run animation
Re-run animation	In an equilateral triangle medians, heights, mediators and bisectors are the same . They are concurrent at a point at both center of gravity,, orthocenter , center of the circle and center of the inscribed circle of triangle ABC.