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 diagram below to enlarge it.
Consider rotation anti-clockwise 90° about M, then D→C and F→B.Thus ΔMDF→ΔMCB and hence congruent. The result S₁+S₃=S₂+S₄ then follows.
Tr.s MBC & MFD are congruent SAS hence they are equal in area and the result followsSumith PeirisMoratuwaSri Lanka
Problem 1224Let area triangle ABC is (ABC).Then (BMC)=(ABM) (BM=MC). But <BMA+<DMF=180 so(MDF)/(ABM)=(MF.MD)/(BM.AM)=1.So (BMC)=(MDF) or S_1+(MHPQ)+S_(3 ) =S_2 +(MHPQ)+S_4.Therefore S_1+S_(3 )=S_2+S_4.APOSTOLIS MANOLOUDIS 4 HIGH SCHOOL KORYDALLOS PIRAEUS GREECE