3. Proposition I.6 is the converse of Thales' theorem about the base angles of an isoceles triangle being equal which is Proposition I.5 of the Elements. Proposition I.6 is the first time in Elements...

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Extracted text: 3. Proposition I.6 is the converse of Thales' theorem about the base angles of an isoceles triangle being equal which is Proposition I.5 of the Elements. Proposition I.6 is the first time in Elements that Euclid uses proof by contradiction, reductio ad absurdum. Complete the following proof by showing that ADBC is congruent to AACB which contradicts the fact that ADBC is inscribed within AACB. As Euclid would put it the less cannot be equal to the greater. Technically this is a double reductio ad absurdum argument and you must also show that the second case where AB < ac="" also="" leads="" to="" a="" contradiction.="" you="" may="" finish="" this="" argument="" with="" the="" tried="" and="" true="" "it="" can="" be="" shown="" by="" a="" similar="" argument="" that="" the="" assumption="" ab="">< ac="" also="" leads="" to="" a="" contradiction="" therefore..="" proposition="" i.6="" if="" two="" angles="" in="" a="" triangle="" are="" equal="" the="" sides="" opposite="" these="" angles="" are="" also="" equal.="" a="" proof="" assume="" aabc="" has="" zb="2C" but="" ab="" +="" ac.="" then="" either="" ab=""> AC or AB < ac.="" assume="" ab=""> AC. Then we construct a point D on AB so that DB = AC. B