Technical drawing
EQUIVALENCES
We say that two figures are equivalent, when they have the same area.
Drawing of a square equivalent to a rectangle.
We add the two unequal sides of the rectangle, and find its proportional mean. This average is the side of the equivalent square.
We calculate their areas.
We check that they have the same areas.
DRAWING OF A RECTANGLE EQUIVALENT TO A TRIANGLE
The area of a quadrilateral is base by height.
The area of a triangle is equal to the base times the height, divided by 2.
Therefore, we divide the height of the triangle into two equal parts, to form the rectangle.
DRAWING OF A SQUARE EQUIVALENT TO A TRIANGLE.
Once the rectangle is obtained, the square equivalent to the triangle is directly found by means of a proportional average.
We add the two unequal sides of the rectangle.
The midpoint (or mediatrix) is traced. With center at that midpoint, and radius to the end of the sum segment, half circumference is drawn.
By the point of union of the two segments, B, a perpendicular rises.
The length of that perpendicular, B G, is the value of the side of the square, which is the proportional mean.
We have found a square equivalent to a triangle.
EQUIVALENT TRIANGLES
The area of a triangle is equal to the base times the height, divided by 2.
For two or more triangles to be equivalent to each other, they must maintain the measurements of their base and height.
All the upper vertices of these triangles are contained in a line parallel to the base.
Therefore, all the triangles formed in this example are equivalent, because they have the same height and the same base.