## Euclid, Elements of Geometry, Book I, Proposition 38 (Edited by Dionysius Lardner, 1855)

Proposition XXXVIII. Theorem.
[Euclid, ed. Lardner, 1855, on Google Books]

 (169) Triangles on equal bases and between the same parallels are equal.

For by the same construction as in the last proposition they are shown to be the halves of parallelograms on equal bases and between the same parallels.

(170)   Cor. 1.—Hence a right line drawn from the vertex of a triangle bisecting the base bisects the area.

This proves that if two triangles have two sides respectively equal, and the included angles supplemental, the areas will be equal; for the two triangles into which the bisector of the base divides the triangle are thus related.

(171)   Cor. 2.—In general, if the base of a triangle be divided into any number of equal parts (161) lines drawn from the vertex to the several points of division will divide the area of the triangle into as many equal parts.

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Previous: Proposition 37

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