Question

Is a quadrilateral with vertices , , , and . the slope for is . the slope for is . the slope for is . the slope for is . so, ______. therefore, is a parallelogram. what is the missing step in the proof?

1) The opposite sides are parallel
2) The opposite sides are equal in length
3) The opposite angles are equal
4) The diagonals bisect each other

Answer 1

The missing step in the proof involves confirming that opposite sides are parallel, which is verified through the equality of slopes.

Step-by-step explanation:

The missing step in the student's proof that a quadrilateral is a parallelogram concerns the slopes of its sides. The slopes of opposite sides of a quadrilateral are compared to determine if they are parallel. If opposite sides have the same slope, they are parallel. In a parallelogram, both pairs of opposite sides must be parallel. Since the slopes of opposite sides match, step 1 is the correct answer: The opposite sides are parallel.