Triangles and parallelograms which are of the same height are to one another as their bases.
The proportion of areas of triangles (parallelograms) of the same height is equal to the proportion of the lengths of their bases.
Proofs: 1
Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
As is easily demonstrated, this proposition holds even when the triangles, or parallelograms, do not share a common side, and/or are not right-angled (translator's note). ↩