Contents
In this publication, we will consider the main properties of the pyramid (regarding the side edges, faces, inscribed and described in the base of the circle), accompanying them with visual drawings for a better perception of the information presented.
Note: we examined the definition of a pyramid, its main elements and varieties in, so we will not dwell on them in detail here.
pyramid properties
Pyramid with equal side ribs
Property 1
All angles between the side edges and the base of the pyramid are equal.
∠EAC = ∠ECA = ∠EBD = ∠EDB = a
Property 2
A circle can be described around the base of the pyramid, the center of which will coincide with the projection of the top onto its base.
- Point F – vertex projection E on the basis ABCD; is also the center of this foundation.
- R is the radius of the circumscribed circle.
The side faces of the pyramid are inclined to the base at the same angle.
Property 3
A circle can be inscribed at the base of the pyramid, the center of which coincides with the projection of the vertex onto the base of the figure.
Property 4
All heights of the side faces of the pyramid are equal to each other.
EL = EM = EN = EK
Note: for the properties listed above, the reverse formulations are also true. For example, for Properties 1: if all the angles between the side edges and the plane of the base of the pyramid are equal, then these edges have the same length.