1. PYRAMIDS

2. Slicing a Right Rectangular Pyramid with a Plane
A rectangular pyramid with base B and vertex V is the collection of all segments 𝑉𝑃 for any point P in B.
The rectangular pyramid is a solid once the collection all segments 𝑉𝑃 for any point P in B are taken.
The pyramid has a total of 5 faces: four lateral faces and a base.

3. A right rectangular pyramid? Or not?
If the vertex lies on the line perpendicular to the base at its center (the intersection of the rectangle’s diagonals), the pyramid is called a right rectangular pyramid
A right rectangular pyramid NOT a right rectangular pyramid

4. Sketch a right rectangular pyramid from (1) directly over the vertex

5. The view of a right rectangular pyramid from:
directly over the vertex

6. Sketch a right rectangular pyramid from (2) facing straight onto a lateral face

7. The view of a right rectangular pyramid from:
facing straight onto a lateral face

8. Sketch a right rectangular pyramid from (3) the bottom of the pyramid

9. The view of a right rectangular pyramid from:
the bottom of the pyramid

10. Assume the figure is a top-down view of a rectangular pyramid.
Make a sketch of any two lateral faces.
What measurements must be the same between the two lateral faces?

11. The equal sides in each triangle are the same between both triangles.
The heights of the triangles are not equal unless the base is square.

12. Now we are going to look at slices made parallel and perpendicular to the rectangular base of a pyramid.
A slicing plane passes through segment a parallel to base B of the pyramid.
Sketch what the slice will look like.
Then sketch the resulting slice as a 2D figure.

13. The slice is a rectangle.
The slice looks a lot like the rectangular base but is smaller in size.
The slice made parallel to the base of a right rectangular pyramid is a scale drawing, a reduction of the base.
Slices made parallel to the base of a pyramid are rectangles, and are scale drawings of the base.

14. Slice along segment a perpendicular to base B:
What does the slice look like?

15. Slicing a rectangular pyramid perpendicular to its base:
The slice is in the shape of an isosceles trapezoid

16. Slicing a rectangular pyramid through the vertex perpendicular to the base:
The slice is in the shape of a triangle