Problem: Let be the midpoint of side of triangle . Let be a point in between and , and let be drawn parallel to and intersecting at . If the ratio of the area of triangle to that of triangle is designated by , then
Answer Choices:
A. depending upon the position of
B. independent of the position of
C. depending upon the position of
D. depending upon the position of
E. independent of the position of
Solution:
Since is the midpoint of , the area of triangle the area of triangle . But the area of the area of the area of , and in area (they have the same base MD and equal altitudes to this base since MD | PC ). Therefore, in area
independent of the position of between and M. Query; Is the theorem true when is to the left of ?
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