Final answer:
Similar polygons have the same shape but may differ in size, making statement A true and B false. Statement C is false as rectangles must have the same aspect ratio to be similar, while D is true because all squares are inherently similar. For materials, changes in dimensions due to temperature are proportional to original sizes.
Step-by-step explanation:
Understanding Polygon Similarity and Change in Dimensions
When dealing with the concept of similarity in geometry, it is important to note that similar polygons have the same shape but do not necessarily have the same size. Therefore, statement A is true: If two polygons are similar they have the same shape. This implies that the corresponding angles of similar polygons are equal, and their corresponding sides are proportional in length.
Statement B is incorrect because two similar polygons can have different sizes. This is directly related to the definition of similarity, which allows for proportionality but not equality of size.
Statement C is false because not all rectangles are similar; they must have the same aspect ratio (ratio of length to width) to be similar. However, statement D is true: All squares are similar. A square is a special type of rectangle with all sides of equal length and all angles equal to 90 degrees. Therefore, all squares will have sides that are proportional and the same internal angles, making them similar regardless of their size.
Looking at the change of dimensions due to temperature change in materials, if the original cross-sectional area and height are different in two blocks of the same material, the change in these dimensions will be proportional to the original dimensions. Therefore, if Block B has twice the size of each dimension compared to Block A, the change in volume, cross-sectional area, and height for Block B will also be twice that in Block A, assuming the expansion is uniform.