Online Geometry theorems, problems, solutions, and related topics.
Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the figure below to enlarge the problem 946.
let's take the informal pragmatic approach: if the problem statement does not depend on A, B, C, D position but only on quadrilateral area, it holds for a particular case where, say, B=C=E. In this degenerate configuration, it's easy to see that area(CEFH) = area(ABCD)/4 = 7. Hence this must hold for *any* ABCD ;-)bleaug
Let S(ABC) denote the area of ABC, and so on. Since EF//BD//GH, so S(CEHF) = S(CEGF). Consider quadrilateral CEGF. CE = 1/2 CBEG = 1/2 BAGF = 1/2 DAFC = 1/2 DCSo CEGF~CBAD. Hence, S(CEHF) = S(CEGF) = 1/4 S(CBAD) = 7