document.write( "Question 1176856: Prove this using indirect proof in two-column form.
\n" ); document.write( "Given: 𝑀𝑃 ⊥ ̅NO
\n" ); document.write( "Prove: ∠NPM is not a straight angle
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Prove this using indirect proof in two-column form.
\n" ); document.write( "Given: $\"MP\"$ ⊥ ̅ $\"NO\"$
\n" ); document.write( "Prove: ∠ $\"NPM\"$ is not a straight angle\r
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\n" ); document.write( "\n" ); document.write( "statement........................................................reason\r
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\n" ); document.write( "\n" ); document.write( "1) ∠ $\"NPM+\"$ is a straight angle ...........1) Assumpe opposite\r
\n" ); document.write( "\n" ); document.write( "2) m∠ $\"NPM+=+180\"$ °.................... 2) Definition of a striaght angle\r
\n" ); document.write( "\n" ); document.write( "3) $\"MP+\"$ ⊥ ̅ $\"NO\"$ ....................................3) Given\r
\n" ); document.write( "\n" ); document.write( "4) ∠ $\"NPM\"$ is a right angle................. 4) definition of perpendicular lines\r
\n" ); document.write( "\n" ); document.write( "5) m ∠ $\"NPM+=+90\"$ }°.................... 5) definition of a right angle\r
\n" ); document.write( "\n" ); document.write( "6) m ∠ $\"NPM\"$ is not a straight angle................ contradiction of steps 2 and 5\r
\n" ); document.write( "\n" ); document.write( "7) ∠ $\"NPM\"$ is not a straight angle..................... due to the contradiction between 2 and 5, we know that the assumption that WE INTRODUCED
\n" ); document.write( "in the first step (∠ $\"NPM\"$ is a straight angle) is $\"false\"$ .
\n" ); document.write( "Therefore, the opposite must be $\"true\"$ : ∠ $\"NPM+\"$ is $\"not\"$ a straight angle\r
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