5.6 Indirect proof &amp; inequal.

# 5.6 Indirect proof &amp;amp; inequal. - 5.6 Indirect Proof...

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5.6 Indirect Proof and Inequalities in 2 Δs Pg 302

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Indirect proof Indirect proof – a proof in which you prove that a statement is true by first assuming that the opposite is true. Steps 1. Assume the prove statement is false 2. Obtain statements that logically follow from your assumption 3. If you find a contradiction, then the original prove stmt must have been true.
Example Given: ΔABC Prove: ΔABC doesn’t have more than one obtuse angle B A C

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Indirect Proof 1. Start by assuming that Δ ABC does have more than one obtuse 2. m A >90 o and m B>90 o (def. of obtuse ) m A + m B > 180 o (+ prop) However, you know that all 3 s must add up to 180 o (Δ sum thm) m A + m B+ m C =180 o m A +m B =180 o – m C (- prop. =) So, you can substitute 180 o - m C for m A +m B in m B +m A >180 180 o - m C>180 0 o > m C (- prop. =) 3. The last statement isn’t possible so you know that Δ

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## This note was uploaded on 02/12/2011 for the course MTG 3212 taught by Professor Jackson during the Spring '11 term at University of Florida.

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5.6 Indirect proof &amp;amp; inequal. - 5.6 Indirect Proof...

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