Euclid Book 1 - Proposition 21
Triangle within a triangle, sides are smaller, angle is greater

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To be proved: If from the ends of one of the sides of a triangle two straight lines are constructed meeting within the triangle, then the sum of the straight lines so constructed is less than the sum of the remaining two sides of the triangle, but the constructed straight lines contain a greater angle than the angle contained by the remaining two sides.

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There is a triangle ABC with a smaller triangle DBC inside, with line BC common.

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© Jo Edkins 2010 - Return to Euclid index