Second Year Mathematics for Secondary Schools

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Thus if we are able to find the area of a parallelogram, the area of the triangle is found. FIG. 245 FIG. 246 Fig. 246 shows how the area of a parallelogram can easily be compared with the area of a rectangle. The question arises, whether the rectangle and the parallelogram of Fig. 246 are equal to each other, and, more generally, under what con- ditions such figures are equal to each other. This question is answered by Exercise i, 229. If we know how to compare parallelograms, we can com- pare... parallelograms with rectangles because a rectangle is a special case of a parallelogram. 228. We have thus the following chain of problems leading to the problem of computing the area of the triangle: (1) to compare parallelograms (2) to compare a parallelogram and a rectangle (3) to compute the area of a rectangle (4) to compute the area of a parallelogram (5) to compare a parallelogram and a triangle (6) to compute the area of a triangle. PROPOSITION I 229. Theorem: Parallelograms having equal bases and equal altitudes are equal.

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