Geometry Problem

Click the figure below to see the complete problem 508 about Triangle with three Squares, Equal Area.

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Complete Problem 508

Level: High School, SAT Prep, College geometry

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## Friday, August 20, 2010

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Problem 508: Triangle with three Squares, Equal Area

See also:

Complete Problem 508

Level: High School, SAT Prep, College geometry

Online Geometry theorems, problems, solutions, and related topics.

Geometry Problem

Click the figure below to see the complete problem 508 about Triangle with three Squares, Equal Area.

See also:

Complete Problem 508

Level: High School, SAT Prep, College geometry

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Paralleogram BGTD => ▲BGT = ▲A3 = ▲A1 see P502

ReplyDelete( ▲M3TG = ▲M3BD, M3 midpoint of DG )

In the same way A2 = A1, A4 = A1

A1=area(ABC)=1/2AB.BC.sin(ABC)=1/2.AB.AC.sin(BAC)=1/2.BC.AC.sin(BCA)

ReplyDeletebut sin(ABC)=sin(DBG) (ABC) supplement to (DBG)

and sin (BAC)=sin(EAJ)

sin(BCA)=sin(FCH)

from above we can conclude that A1=A2=A3=A4

Peter Tran

Rotate triangle CFH 90 deg. around point C.

ReplyDeletePoint F moves on Point B, H moves to H'.

A, C, H' are collinear, and AC=CH', so A1=A4.

Area ABC is (ABC).But <ABC+<DBG=180 so (ABC)/(DBG)=(AB.BC)/(BD.BG)=1 so A1=A3.

ReplyDeleteSimilar A1=A2=A4.