You will need

- pencil;
- - the notebook.

Instruction

1

Find natural size of the triangle it is possible to method of replacing planes of projection. For this geometric figure present in the form of a level plane when one of the patronage displayed without distortion in relation to the plane.

2

First, given the coordinates of points, construct the projection of the triangle ABC. Then slide the front horizontal projection of this triangle characterized by points B2 and M2. After that, a connecting line, find the horizontal projection of the point M1.

3

Below the triangle was projecting an additional plane P4, which is perpendicular to the plane P1. The axis x1,4 should be located perpendicular to the projection of B1M1.

4

From every point of the horizontal plane guide the connection lines perpendicular to the axis x1,4. To convert the triangle in the plane of the level, enter another dimension – P5. The axis x4,5 is located in parallel A4B4C4.

5

From each point A4B4C4 guide the connection lines, which are perpendicular to the axis x4,5. On these lines put the distance equal to the distance from the axis x1,4-horizontal projection of each point.

6

Triangle ABC has taken a position which is parallel to the plane A5. Projection A5B5C5 – the actual size of the triangle ABC.

7

To determine the natural size of the triangle you can also and method of rotation. To do this, first imagine a triangle in a projective plane, then rotate it around a second given axis, converting it to a plane level.

Note

Be careful when constructing the projection of a triangle: if you make a mistake, the result will be incorrect.

Useful advice

The angle formed by the projection of the triangle А4В4С4 and the coordinate axis, - tilt angle of a given triangle ABC to the plane P1.