# Proposition: 1.44: Construction of Parallelograms II

### (Proposition 44 from Book 1 of Euclid's “Elements”)

To apply a parallelogram equal to a given triangle to a given straight line in a given rectilinear angle. * Let $AB$ be the given straight line, $C$ the given triangle, and $D$ the given rectilinear angle. * So it is required to apply a parallelogram equal to the given triangle $C$ to the given straight line $AB$ in an angle equal to (angle) $D$. ### Modern Formulation

Given an arbitrary triangle ($$\triangle{C}$$), an arbitrary angle ($$\angle{D}$$), and an arbitrary segment ($$\overline{AB}$$), it is possible to construct a parallelogram ($$\boxdot{FGBE}$$) equal in area to the triangle $\triangle{C}$ which contains the given angle $\angle {D}=\angle{GBE}$ and has a side $\overline{GB}$ equal in length to the given segment $\overline{AB}$.

Proofs: 1

Proofs: 1 2 3
Sections: 4

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### References

#### Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014