Quadrangular pyramid with transformations

This model allows receivingof all types of the quadrangular pyramid and pentagon. We remind that the transformations are carried out with the help of change of each of the sides separately. Of particular interest is the case when the basement of ABDC quadrate and the lateral edge are perpendicular to the plane of the basement.

Then according to the theorem of three perpendiculars we obtain: AC ⊥CD, which implies AC⊥SC.

It is possible to receive a triangular pyramid from a quadrangular pyramidas follows. All sides of a triangle ABD we extend up to the end, then we hold the top C and shortening SC gradually we put it inside (i.e. top of C) of the triangular pyramid ABDS until SC becomes ⊥ (ABD) and C ∈ (ABD). There is also the second option of transformation.

The top of C ∈ (SAD). As a result we obtain a triangular pyramid ABDS (Fig. 4) in which it is possible to construct the height BC with the help of an auxiliary rod. In the same way it is possible to obtain a triangular pyramid from the quadrangularpyramid. Shortening AD, we do so that the sides of DB and DC made one line to the line BC. It is clear that turning this pyramid, different types of triangular pyramids are created, which are used in the solutions of tasks.

For implementation of each of the following transformations it is necessary to close consistently each of the sides of the model up to the stop. The quadrangular pyramid turns into a regular pentagon with its diagonals.

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