ABC Is Right Angled Triangle.angle B=90degree.if BCDE Is A Square On BC .ACFG Is A Square On AC.

Question

prove AD=BF

Answer 1

????? BC   ???FG    AC

?????BCDE ?????

????ACFG ?????

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Answer 2

Make a sketch of this problem.   Between △CAD and △CFB, CA=CF(2sides of square ACFG), and CD=CB(2 sides of square BCDE).  

And ∠ACD=∠ACB+∠BCD=∠ACB+90° and ∠FCB=∠ACB+∠FCA=∠ACB+90°  So ∠ACD=∠FCB Thus △CAD≡△CFB (SAS).   Therefore AD=BF.   Q.E.D.

Note that AD crosses BF at right angles.  It shows that, when △CFB is turned 90 degrees around point C as the center: CF to CA, and CB to CD, △CFB and △CAD fit together.