Geometry Problem. Post your solution in the comments box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Friday, June 19, 2015

### Geometry Problem 1124: Triangle, Median, Two Squares, Area

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Consider rotation anti-clockwise 90° about M,

ReplyDeletethen 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 follows

ReplyDeleteSumith Peiris

Moratuwa

Sri Lanka

Problem 1224

ReplyDeleteLet 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