Final answer:
If you extend each side of a parallelogram by a distance x, the resulting quadrilateral is a larger parallelogram. Properties such as parallel and equal opposite sides are preserved during the extension.
Step-by-step explanation:
The question pertains to the extension of a parallelogram's sides to create a new quadrilateral. If you extend each side of a parallelogram by an equal length x, the new figure, PQRS, will be a larger parallelogram. Each pair of opposite sides will remain parallel and equal in length, which are defining properties of a parallelogram.
To relate to the references provided:
- Marta's scenario with the squares shows that if a square side is doubled, the area will be four times as large since the area of a square is proportional to the square of its side length.
- Using the Pythagorean theorem, we can establish relationships between the sides of right triangles, which are also applicable to the diagonals of parallelograms if they are right triangles.
- Proportions, as used in the Moon's width problem, are also essential in geometry when making comparisons or establishing properties of figures.