document.write( "Question 197026: Give a detailed proof of the following fact: The line segment joining the midpoints of two sides of a triangle is parrallel to and half the length of the third side. \n" ); document.write( "

Algebra.Com's Answer #147724 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "I'll let you fill in the details, but here is the strategy:\r
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\n" ); document.write( "\n" ); document.write( "Given triangle ABC, P the midpoint of AB, Q the midpoint of BC.\r
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\n" ); document.write( "\n" ); document.write( "Since angle B is angle B and PB:AB = BQ:BC = 1:2 by definition of midpoint, then ABC is similar to PBQ.\r
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\n" ); document.write( "\n" ); document.write( "Use the fact that angle BPQ = angle BAC by similarity of ABC and PBQ and one of the theorems about parallel lines and a transversal to prove that PQ parallel to AC.\r
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\n" ); document.write( "\n" ); document.write( "Then use proportionality of the sides of similar triangles to show that if PB:AB = BQ:BC = 1:2 by definition of midpoint, then PB:AB = BQ:BC = PQ:AC = 1:2.\r
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\n" ); document.write( "\n" ); document.write( "John
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