Online Geometry theorems, problems, solutions, and related topics.
See complete Problem 88Triangle and Quadrilateral Areas, Midpoints. Level: High School, SAT Prep, College geometryPost your solutions or ideas in the comments.
AECN =? DEBMAMB*+AMN**+MBN***+BCN****+S=MBC*+MNC**+MND***+CND****+SAMN**=MNC** ( M midpoint of AC, the same reason for others)S is area of BEC ( common for both )
Solution to problem 88. Looking at quadrilateral ABCD, as it was proved in problem 87, quadrilaterals BCNA and BCDM have the same area. SoS1 = S(AECN) = S(BCNA) + S(BEC) == S(BCDM) + S(BEC) = S(DEBM) = S2.