Hinge Theorem. Let ABC and DEF be triangles such that AB=DE, AC=DF, and measure angel BAC smaller measure angel EDF. Then BC smaller EF.

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Hinge Theorem. Let ABC and DEF be triangles such that  AB=DE, AC=DF, and measure angel BAC smaller measure angel EDF. Then BC smaller EF.

Addison Herman · Accepted Answer

Let   △  A  B  C and   △  D  E  F be two triangles in which   A  B  =  D  E  ,  A  C  =  D  F, and   ∠  C  A  B  &amp;gt;  ∠  F  D  E.Construct   ∠  E  D  G on DE at point D.Place G so that   D  G  =  A  C.Join EG and FG.Since   A  B  =  D  E  ,  ∠  B  A  C  =  ∠  E  D  G, and   A  C  =  D  G  ,  B  C  =  G  E.By Euclid&#039;s first common notion,   D  G  =  A  C  =  D  F.Thus,   ∠  D  G  F  =  ∠  D  F  G  .So by Euclid&#039;s fifth common notion,   ∠  E  F  G    &amp;gt;    ∠  D  F  G  =  ∠  D  G  F    &amp;gt;    ∠  E  G  F.Since   ∠  E  F  G  &amp;gt;  ∠  E  G  F  ,  E  G  &amp;gt;  E  F.Therefore, because   E  G  =  B  C  ,  B  C  &amp;gt;  E  F.

Hinge Theorem. Let ABC and DEF be triangles such that AB=DE, AC=DF, and measure angel BAC smaller measure angel EDF. Then BC smaller EF.

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