document.write( "Question 252915: explain why it is necessary for two congruent angles to be in the same triangle in order for the sides opposite them to be congruent \n" ); document.write( "
Algebra.Com's Answer #185041 by drk(1908)\"\" \"About 
You can put this solution on YOUR website!
This seems like an explanation of the isosceles triangle theorem.
\n" ); document.write( "THEOREM 1: If two angles of a triangle are congruent then their opposite sides are congruent.
\n" ); document.write( "THEOREM 2: If two sides of a triangle are congruent then their opposite angles are congruent.
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\n" ); document.write( "THEOREM 1:
\n" ); document.write( "given: two angles of a triangle are congruent.
\n" ); document.write( "prove: opposite sides of the triangle are congruent.
\n" ); document.write( "STATEMENT 1: triangle ABC
\n" ); document.write( "REASON 1 : given
\n" ); document.write( "STATEMENT 2: angle B congruent angle C.
\n" ); document.write( "REASON 2: given
\n" ); document.write( "STATEMENT 3: construct ray AD such that it is an altitude of triangle ABC.
\n" ); document.write( "REASON 3: definition of construction.
\n" ); document.write( "STATEMENT 4: angles BDA and CDA are right angles
\n" ); document.write( "REASON 4: definition of altitude.
\n" ); document.write( "STATEMENT 5: AD congruent AD
\n" ); document.write( "REASON 5: reflexive property of equality.
\n" ); document.write( "STATEMENT 6: triangle BDA congruent triangle CDA
\n" ); document.write( "REASON 6: AAS postulate
\n" ); document.write( "STATEMENT 7: AB congruent AC
\n" ); document.write( "REASON 7: CPCTC.
\n" ); document.write( "--
\n" ); document.write( "The proof of THEOREM 2 will be similar.
\n" ); document.write( "hope that helps. \n" ); document.write( "
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