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Euclid's Proposition 6 - If in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another.
- Assume by way of contradiction that the length of the sides AC an BC are not equal. Then one of the sides must longer. Let that side be AC
- Now draw a point D on AC such that the length of AD is equal to the length of BC.
- Since DA equals CB, the side AB is in common, and angle DBA is equal to angle DAB by definition, the triangle ACB is congruent to the triangle ADB, so DB must equal CB, which is a contradiction.
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