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

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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.