Final answer:
Quadrilaterals LMNO and ABCD being congruent means they have equal shape and size, with matching sides and angles. Also, when the side length of a square is doubled, its area becomes four times larger because the area of a square is the square of its side length. Congruence and similarity are key concepts in geometry.
Step-by-step explanation:
Since quadrilaterals LMNO and ABCD are congruent, we can conclude that they are equal in shape and size. This means that all corresponding sides and angles of LMNO match those of ABCD one to one. This is an essential property of congruent figures. For example, if the side length of each square on the grid is one unit, each corresponding side of the two congruent quadrilaterals will have lengths that are whole number lengths, as they must be composed of a whole number of these unit squares.
When comparing the areas of squares like those mentioned for Marta, if one square has a side length that is double that of another, its area will be four times larger because the area is calculated as the side length squared (area = side length ²). The relationship between the areas of similar figures is always the square of the ratio of their corresponding lengths. Therefore, in the example of Marta's squares, since the side length ratio is 2:1, the area ratio will be 4:1.
The concept of congruence also extends to other shapes and dimensions. For instance, congruent triangles will have the same angles and side lengths, while in three dimensions, congruent cubes will have equal edge lengths, surface areas, and volumes. The properties of congruent and similar figures are fundamental in geometry, which can be applied to solve various real-world problems.