Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 98Quadrilateral Areas, Centroids, Similarity. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
1. Let the mid-pt of AD be M, MH:HB=MG:GC=1:2, so HG//BC, so are the others.2. considering the parallel sides, observe that ABCD is similar to FGHE. S1/S=(HG/BC)^2=(MH/MB)^2=(1/3)^2=1/9
(Remark for 2.)also require to consider ratio in order to prove the similarity