Final answer:
The missing statement in step 5 should imply a negative reciprocal relationship between the slopes of AB and XY, necessary for them to be perpendicular. The most adequate option would be the rise of one line equaling the negative of the run of the other, which is not directly given but suggested by Option B and is needed for their slopes to multiply to -1.
Step-by-step explanation:
The missing statement in step 5 for proving that the slope of AB × the slope of XY = -1 requires the understanding that if lines AB and XY are perpendicular, then the product of their slopes must be -1. Since triangles ABC and XYZ are similar by the given information, we know that the slopes of corresponding sides will be equal, which handles the condition for similarity but does not directly address perpendicularity.
However, the assertion that the slope of AB × the slope of XY = -1 suggests that AB is perpendicular to XY, which also means their respective rises and runs relate to one another in a particular way. Since the slope is defined as 'rise over run', for two lines to be perpendicular, the rise of one must be the negative reciprocal of the run of the other and vice versa, making them negative inverses. This gives us:
- A. rise of AB = run of XY
- B. rise of XY = run of AB
- C. rise of AB = rise of XY
- D. run of AB = run of XY
To satisfy the condition that the product of slopes is -1, we need the rise of one line to be the negative of the run of the other (negative reciprocal relationship). Therefore, the correct missing statement is Option B: "rise of XY = run of AB and rise of AB = -run of XY", which is not explicitly listed but is implied for the product of their slopes to equal -1.