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TRANSFORMATION OF A POLYGON

STEP 1

It is possible to transform any convex polygon with n sides into a polygon with n-1 sides that has the same area. Try the proof by yorself following the steps as described below: 1) Draw a polygon with five sides 2) Label its vertexes A, B, C, D, E, F, G anticlockwise 3) Draw , for instance, the diagonal AC and the parallel line r through B to AC 4) Label with F the intersection between r and the extension of CD 5) Prove that the triangle ABC is equivalent to AFC using the tool Area Toolbar Image. Now the 5-sides polygon as been transformed in a 4-sides polygon of equivalent area. 6) Following the same steps as previous described, try to transform the 4-sides polygon into a triangle. 7) Finally, prove, using the tool area, that the triangle has the same area of the 5-sides polygon.

8) Explaine the geometrical reasons of point 5.

6) Following the same steps as previous described, try to transform the 4-sides polygon into a triangle, such that you can proof that any poligon can be transformed in a triangle. 7) Finally, prove, using the tool area, that the triangle has the same area of the 5-sides polygon.