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$??解：相似，理由如下：??$

$??因?yàn)锳B=30，BC=39 ， AC=18，??$

$??A'B'=20，B'C'=26，A'C'=12??$

$??所以\frac {AB}{A'B'}=\frac {BC}{B'C'}=\frac {AC}{A'C'}=\frac {3}{2}??$

$??所以△ABC∽△A'B'C'??$

$??解：(1)相似，理由如下：??$

$??因?yàn)椤螦=45°， AB=12\ \mathrm {cm}，AC=15\ \mathrm {cm}，??$

$??∠A'=45°， A'B'=16\ \mathrm {cm}，A'C'= 20\ \mathrm {cm}??$

$??所以\frac {AB}{A'B'}=\frac {AC}{A'C'}=\frac {3}{4}，∠A=∠A'??$

$??所以△ABC∽△A'B'C'??$

$??(2)相似，理由如下：??$

$??因?yàn)锳B=12\ \mathrm {cm}，BC=15\ \mathrm {cm} ， AC=24\ \mathrm {cm}，??$

$??A'B'=20\ \mathrm {cm}，B'C'=25\ \mathrm {cm}，A'C'=40\ \mathrm {cm}??$

$??所以\frac {AB}{A'B'}=\frac {BC}{B'C'}=\frac {AC}{A'C'}=\frac {3}{5}??$

$??所以△ABC∽△A'B'C'??$

$??證明：(1)因?yàn)閈frac {AB}{AD}=\frac {BC}{DE}=\frac {AC}{AE}??$

$??所以△ABC∽△ADE??$

$??所以∠BAC=∠DAE??$

$??所以∠BAD=∠CAE??$

$??因?yàn)閈frac {AB}{AD}=\frac {AC}{AE}，∠BAD= ∠CAE??$

$??所以△ABD∽△ACE??$

$??(2)因?yàn)椤鰽BD∽△ACE??$

$??所以∠ABD=∠ACE?$

?

$??解：設(shè)另外兩邊長分別為x，y??$

$??①\frac {2}{4}=\frac {x}{5}=\frac {y}{6}??$

$??解得，x=\frac {5}{2}，y=3??$

$??②\frac {2}{5}=\frac {x}{4}=\frac {y}{6}??$

$??解得，x=\frac {8}{5}，y=\frac {12}{5}??$

$??③\frac {2}{6}=\frac {x}{4}=\frac {y}{5}??$

$??解得，x=\frac {4}{3}，y=\frac {5}{3}??$

$??綜上所述，另外兩邊長分別為\frac {5}{2}，3或\frac {8}{5}，\frac {12}{5}或\frac {4}{3}，\frac {5}{3}??$

$??所以選料不唯一??$

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