prove that the diagonals of a regular hexagon divides it into 6 equilateral triangles
Answers
How do I prove a regular hexagon is made up of 6 equilateral triangles?
A regular hexagon has six equal sides.
The six sides of the regular hexagon with the two sides connecting them to the center, for six triangles.
The regular hexagon has 6 exterior angles and each one of them is 360/6 = 60 degrees.
The 6 interior angles of the hexagon are supplementary to the exterior angle and are 120 deg. And there are two angles that form the interior angle. And they are the base angles of two different triangles. That is, each of the base angles is 60 degrees.
The six triangles have a common center which is the vertices of the 6 triangles clustered together. Therefore the angles at the center is 360/6 = 60 degrees for each triangle.
So all three angles of the six triangles are 60 deg each.
So there are 6 equilateral triangles that form the regular hexagon.
I think you can prove this now