Final answer:
The statement is false. A dilation with a scale factor of ¾ does not result in a congruent quadrilateral. Instead, it creates a similar quadrilateral with proportional side lengths.
Step-by-step explanation:
True or false if you dilate quadrilateral ABCD with center A and scale factor ¾ gives a quadrilateral that is congruent to EFHG. This can be shown with a translation of A to E and then a rotation with center E.To determine if this statement is true or false, we need to consider the properties of dilations and congruent figures. A dilation with a scale factor of ¾ enlarges or reduces the size of a figure by multiplying the lengths of all sides by the scale factor. If two figures are dilations of each other, they are similar (not congruent) and have proportional side lengths.Therefore, the given statement is false. A dilation with a scale factor of ¾ does not result in a congruent quadrilateral. Instead, it creates a similar quadrilateral with proportional side lengths.