document.write( "Question 463932: Prove that if two angles are complements of the same angle, then the angles must be congruent. ( Use a paragraph proof ) Given: ∠ 1 and ∠ 2 are complementary. ∠ 2 and ∠ 3 are complementary. Prove: ∠ 1 ≅ ∠ 3 \n" ); document.write( "

Algebra.Com's Answer #317782 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
angle 1 is complement to angle 2
\n" ); document.write( "angle 2 is complement to angle 3
\n" ); document.write( "prove angle 1 is congruent to angle 3\r
\n" ); document.write( "\n" ); document.write( "angle 1 + angle 2 = 90 degrees (definition of complement)
\n" ); document.write( "angle 2 + angle 3 = 90 degrees (definition of complement)\r
\n" ); document.write( "\n" ); document.write( "angle 1 + angle 2 = angle 2 + angle 3 (substitution)\r
\n" ); document.write( "\n" ); document.write( "subtract angle 2 from both sides of the equation.\r
\n" ); document.write( "\n" ); document.write( "you are left with angle 1 = angle 3.\r
\n" ); document.write( "\n" ); document.write( "the geometric explanation is the subtraction property.\r
\n" ); document.write( "\n" ); document.write( "if a = b then a-c = b-c\r
\n" ); document.write( "\n" ); document.write( "the a was angle 1 + angle 2 = 90 degrees
\n" ); document.write( "the b was angle 2 + angle 3 = 90 degrees\r
\n" ); document.write( "\n" ); document.write( "the c was the subtraction of angle 2\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );