Question

two different cross sections are taken parallel to the base of a three-dimensional figure. the theo cross sections are the same shape but are not congruent. what is the three-dimensional figure?

Answer 1

Cone, Triangular Pyramid, and Square Pyramid

Explanation:

Given is that two different cross sections are taken parallel to the base of a three-dimensional figure. The cross sections are the same shape but are not congruent.

In these three shapes, namely cone, triangular pyramid and square pyramid, the cross sections can look same but they are not congruent as the dimensions varies uniformly from one end to the other end.

Answer 2

same shape => similar.

The sections could be either great or smaller in area.

The possible figures could be:
1. A cone (all sections are circles)
2. A truncated cone (all sections are circles)
3. A hemisphere (all sections are circles)
4. A pyramid of any base (triangle, square, pentagon,....)
5. A truncated pyramid of any base (triangle, square, pentagon,....)
There are still other less conventional shapes, but I suppose the above options should suffice.