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Answer :
Final answer:
Given the properties of dilation, the ratios of corresponding sides and perimeters of trapezoid WXYZ and W’X’Y’Z’ are proportional. They are not, however, congruent. The area of the trapezoid W’X’Y’Z’ could be greater or smaller than WXYZ, depending on the dilation factor.
Explanation:
You are asking about the properties of a trapezoid under dilation, specifically trapezoid WXYZ and its image W’X’Y’Z’. In dilation, the figure changes its size but keeps its general shape. So the assertion I: 'The ratios of corresponding sides of trapezoid WXYZ and W’X’Y’Z’ are proportional', is correct. This is because dilation alters the size but not the shape. Thus, the ratios of corresponding sides remain the same.
II: 'The area of trapezoid W’X’Y’Z’ is greater than the area of trapezoid WXYZ'. This may or may not be correct depending on the dilation factor. If the trapezoid is dilated by a factor greater than 1, then the area of the dilated trapezoid will indeed be larger. But if the dilation factor is less than 1, then the area of the dilated trapezoid would be less than the original. So, we can't decisively say if this assertion is correct.
III: 'Trapezoid WXYZ is congruent to trapezoid W’X’Y’Z’'. This is not correct because congruence involves preserving all distances and angles, which means congruent shapes are of the same size. Since dilation involves a change in size, the figures are not congruent.
IV: 'Trapezoid WXYZ and trapezoid W’X’Y’Z’ perimeters are proportional'. This is correct because the lengths of all corresponding sides are increased or decreased by the same factor in a dilation, meaning the perimeter would be proportionally changed.
Therefore, the correct answer would be 'I and IV'.
Learn more about Dilation of Geometric Figures here:
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