In this publication, we will consider the definition and common types of a pyramid with a side edge perpendicular to the base. The presented information is accompanied by visual drawings for better perception.
The definition of such a figure lies directly in its name. This is, in which one of the side ribs forms a right angle with the base plane (i.e. equal to 90 °).
The most common varieties of this pyramid are triangular and quadrangular. Let’s consider them in more detail.
triangular pyramid
- The base is a triangle ABC (can be arbitrary, isosceles, rectangular or equilateral).
- Edge BE perpendicular to base ABC; is the height of the pyramid (h).
- ⦟ABE и ⦟CBE – straight lines, i.e. are equal to 90°.
- Edge ABE и EPC are right triangles.
- Edge AEC inclined to the plane of the base at an angle α (⦟EMB).
quadrangular pyramid
- Base: rectangle, square, parallelogram or rhombus.
- Edge AE located at right angles to the base ABCD; is the height of the figure (h).
- Edge ADE и ABE are right triangles.
If the base of such a pyramid is a square or a rectangle, then ⦟CDE и ⦟CBE are equal to 90°. Those. all side faces of the figure are right triangles.
Note: sometimes a pyramid with a side edge perpendicular to the base is erroneously called rectangular. This can only be true if one of its vertices has 3 right angles (as, for example, in the figure above).