So ΔOAB and ΔOCB are congruent triangles by the Side-Angle-Side postulate, and ΔOCB is an identical equilateral triangle to ΔOAB. ∠ABO≅∠CBO (definition of congruent angles) M∠ABO=m∠CBO=60° as BO is the angle bisector Now let's connect O with vertex C, and compare triangles ΔOAB and ΔOCBĪB=BC as equal sides of a regular hexagon And from the sum of angles in a triangle, ∠AOB is also a 60° angle, and ΔOAB is an equilateral triangle. The angle bisectors create two half angles which measure 60°: m∠OAB=m∠OBA=60°. It is easy to see that ΔOAB is equilateral - m∠BAF = m∠ABC = 120°, as interior angles of a regular hexagon. Let's draw the angle bisectors of two adjacent interior angles, and call their point of intersection O: So let's formally prove this intuitive result.

Many of the 'proofs' I've seen that show that a regular hexagon is comprised of six equilateral triangles start with things like 'Draw a circle that passes through the regular hexagon's vertices' - but they do not prove that you can actually draw such a circle (it's possible to do this, of course, but it is rather complex). A regular hexagon is comprised of six equilateral triangles From this we derive many other interesting properties, starting with showing that a regular hexagon is made up of 6 equilateral triangles.

And since all the interior angles of a regular hexagon are equal, each one measures 720°/6=120°. In a hexagon, n=6, so the sum of the interior angles in a hexagon is (6-2)

180°, where n is the number of sides of the polygon.

Interior Angles of a Regular Hexagonįor any polygon, the sum of the interior angles is S=(n-2) A regular hexagon has six sides, which are all equal, and six equal interior angles.

What is a Regular Hexagon?Ī regular polygon is a two-dimensional convex shape whose sides and interior angles are all equal. We will look at its angles, and find formulas for its perimeter and area using its side or radius. In this post, we'll take a closer look at a regular hexagon - a six-sided polygon where all the sides are equal.

Perfect hexagon