Explanation:
- E is the midpoint of AB
- F is the midpoint of CB
- EF is the midline of ΔABC, hence ║AC
- H is the midpoint of AD
- G is the midpoint of CD
- GH is the midline of ΔACD, hence ║AC
- length of EF = length of GH = 1/2 length of AC
- EFGH is a parallelogram
- ΔEBF ~ ΔABC
- ΔHGD ~ ΔACD
- area relationships can be derived from the fact that the similar triangle scale factors are 1:2
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Similar relationships pertain to the diagonal BD and segments EH and FG. You can also conclude that area EFGH is half of area ABCD by considering the various triangles you get by connecting midpoints different ways.
