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Dividing a Triangle by Lines Parallel to Two Sides

​
E
S
1
≈
5.26
S
2
≈
18.45
S
3
≈
19.70
2
S
1
×
S
2
≈
19.70
Let ABC be a triangle and E a point on AC. Let D be on AB such that DE is parallel to BC and F be on BC such that EF is parallel to AB. Let
S
1
,
S
2
, and
S
3
be the areas of ADE, EFC, and DEFB, respectively. Then
S
3
=2
S
1
×
S
2
.
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