document.write( "Question 1195053: Given: ∆ABC, median 𝐴𝐷, AD = 1⁄2 BC
\n" ); document.write( "Prove: ∆ABC is a right triangle, and 𝐵𝐶 is its hypotenuse (in two column proof)
\n" ); document.write( "Statements:
\n" ); document.write( "1.) 𝐴𝐷 is a median, AD = 1⁄2 BC
\n" ); document.write( "2.) CD = DB
\n" ); document.write( "3.) CD = AD
\n" ); document.write( "4.) m∠C = m∠CAD = x
\n" ); document.write( "5.) DB = AD
\n" ); document.write( "6.) m∠B = m∠DAB = 𝑦
\n" ); document.write( "7.) m∠A = x + y
\n" ); document.write( "8.) m∠A + m∠𝐵 + m∠𝐶 = 180
\n" ); document.write( "9.) (x + y) + x + y = 180
\n" ); document.write( "10.) 2x + 2y = 180
\n" ); document.write( "11.) x+y=90
\n" ); document.write( "12.) m∠A=m∠CAD+m∠𝐷𝐴𝐵=x+y=90
\n" ); document.write( "13.) ∠A is a right angle
\n" ); document.write( "14.) ∆ABC is a right triangle
\n" ); document.write( "15.) 𝐵𝐶 is its hypotenuse. \n" ); document.write( "
Algebra.Com's Answer #827395 by Edwin McCravy(20077)\"\" \"About 
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document.write( "Given: ∆ABC, median 𝐴𝐷, AD = 1⁄2 BC\r\n" );
document.write( "Prove: ∆ABC is a right triangle, and 𝐵𝐶 is its hypotenuse\r\n" );
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document.write( "I will draw the triangle a little \"off\", so that what we are to prove\r\n" );
document.write( "does not look quite true.  That way, when creating proofs, we aren't\r\n" );
document.write( "tempted to assume something to be known that isn't, just because it\r\n" );
document.write( "looks true.\r\n" );
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document.write( "∠A in the proof, is really ∠BAC, marked with the red arc, and is\r\n" );
document.write( "the sum of ∠CAD, whose measure is labeled \"x\", and ∠BAD, whose measure\r\n" );
document.write( "is labeled \"y\".\r\n" );
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document.write( "Statements:\r\n" );
document.write( "1.) 𝐴𝐷 is a median, AD = 1⁄2 BC  | Given\r\n" );
document.write( "2.) CD = DB                      | Definition of \"median\" \r\n" );
document.write( "3.) CD = AD                      | Given AD = 1⁄2 BC, and CD = 1⁄2 BC  \r\n" );
document.write( "4.) m∠C = m∠CAD = x              | Renaming measures of angles\r\n" );
document.write( "5.) DB = AD                      | Things = the same thing are =\r\n" );
document.write( "6.) m∠B = m∠DAB = 𝑦              | Renaming measures of angles\r\n" );
document.write( "7.) m∠A = x + y                  | Measures of wholes = sum of measures of\r\n" );
document.write( "                                   their parts\r\n" );
document.write( "8.) m∠A + m∠𝐵 + m∠𝐶 = 180o      | Sum of measures of angles of any ∆ is 180o  \r\n" );
document.write( "9.) (x + y) + x + y = 180o       | Substitution of ='s for ='s\r\n" );
document.write( "10.) 2x + 2y = 180o              | Addition \r\n" );
document.write( "11.) x+y=90o                     | Division of both side by 2\r\n" );
document.write( "12.) m∠A=m∠CAD+m∠𝐷𝐴𝐵=x+y=90o    | Measures of wholes = sum of measures of\r\n" );
document.write( "                                   their parts \r\n" );
document.write( "13.) ∠A is a right angle         | An angle with measure 90o is a right angle\r\n" );
document.write( "14.) ∆ABC is a right triangle    | An triangle with a right angle is a right\r\n" );
document.write( "                                 | triangle\r\n" );
document.write( "15.) 𝐵𝐶 is its hypotenuse.       | The side opposite the right angle of a\r\n" );
document.write( "                                 | right triangle is its hypotenuse.\r\n" );
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document.write( "Edwin
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