Geometry(Guide 3), Chapter 9, Problem 6

[arbabrahman]

I have a query regarding this problem. In the solution ,EFCD is sown as a rhombus. I could not figure out how this conclusion was reached. WOuld someone please explain ..

[tommywallach]

Once you know that BC = CD and BC is parallel to DF, you know that F is the midpoint of BE. From here, everything proceed logically (as laid out in the book). Everything in the shape is divided into equal pieces. If it helps, turn triangle ABE into a square (ABDE). Now you can see the bottom half of the quadrilateral BCDF (the one asked about in Column B) is equal to half of triangle ABE. So the question becomes: "Is triangle BCD also equal to half of triangle ABE." If all the mini triangles built here (as in the explanation) are equal, than the answer must be yes.

-t

[arbabrahman]

Thanks for the explaination

[tommywallach]

Happy to help!

-t