(AF)(BD)(EC) = 2.27 cubic inches and (FB)(DC)(EA) = 2.27 cubic inches.
Thus,
We will use similar triangles to prove this. To construct the similar
triangles, draw two lines parallel to segment FC. One through point B, and
the other through point A.
Notice that there are several pairs of similar triangles.
1. If two parallel lines are cut by a transversal (a line that intersects two or more lines in the same plane at distinct points), then the alternate interior angles are congruent, the alternate exterior angles are congruent, and the corresponding angles are congruent.
2. Vertical angles are congruent.
3. AA ~ AA. If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
4. Corresponding sides of similar triangles are proportional segments.
so,
so,
.
Thus,
.
Hence,
.
We see that
Thus,
Next, just subtitute.
and to obtain
Click here (for GSP file)
to move P or here to change
the triangle.