The surface of a pyramid is a surface of a polyhedron. Each its side represents the plane therefore the section of the pyramid set by a secant the plane is the broken line consisting of separate straight lines.
It is required to you
- - a pencil, - a ruler, - compasses.
Instruction
1. Build the line of crossing of a surface of a pyramid with the frontal projecting plane Σ (Σ2). At first note points of required section which can be defined without auxiliary secants of the planes.
2. The plane Σ crosses the pyramid basis on a straight line 1-2. Note points 12≡22 – a frontal projection of this straight line – and by means of the vertical communication line construct their horizontal projections 11.21 on the parties of the basis of A1C1 and B1C1
3. The edge of a pyramid of SA(S2A2) crosses the plane Σ (Σ2) in a point 4(42). On a horizontal projection of an edge of S1A1 by means of the communication line find a point 41.
4. Through a point 3(32) carry out the horizontal plane of the G(G2) level as an auxiliary secant of the plane. It is parallel to the plane of projections P1 and in section with a surface of a pyramid will give the triangle similar to the pyramid basis. On S1A1 note E1 point, on S1C1 – K1 point. Draw the lines parallel to the parties of the basis of a pyramid of A1B1C1, and on an edge of S1B1 find a point 31. Having connected points 11, 21, 41, 31, receive a horizontal projection of required section of a surface of a pyramid the set plane. The frontal projection of section coincides with a frontal projection of this plane Σ (Σ2).
5. On S1A1 note E1 point, on S1C1 – K1 point. Draw the lines parallel to the parties of the basis of a pyramid of A1B1C1, and on an edge of S1B1 find a point 31. Having connected points 11, 21, 41, 31, receive a horizontal projection of required section of a surface of a pyramid the set plane. The frontal projection of section coincides with a frontal projection of this plane Σ (Σ2).
6. Thus, the problem is solved, proceeding from the principle of accessory of the found points at the same time to two geometrical elements – surfaces of a pyramid and the plane set by a secant Σ (Σ2).