Question

The slope of EF is .


Which statements are true? Check all that apply.

EH is parallel to FG.
EF is perpendicular to EH.
HG is neither parallel nor perpendicular to FG.
Quadrilateral EFGH is a rectangle because it is a parallelogram with four right angles.
Quadrilateral EFGH is a trapezoid because it has exactly one pair of parallel opposite sides.

Answer 1

I’m missing the slope value and/or the diagram/coordinates for E, F, G, H. Can you paste the slope (it looks cut off in your message) or upload the figure or the coordinates of the vertices?

How to decide once I have that info:
- If EFGH is a parallelogram in order E–F–G–H, then opposite sides are parallel: EF ∥ GH and FG ∥ EH.
- Two lines are parallel ⇔ their slopes are equal.
- Two nonvertical lines are perpendicular ⇔ their slopes are negative reciprocals (m1·m2 = −1). A vertical line (undefined slope) is perpendicular to any horizontal line (slope 0).
- A rectangle is a parallelogram with one right angle (equivalently four right angles). So show one adjacent pair of sides are perpendicular.
- A trapezoid has exactly one pair of parallel sides; a parallelogram has two pairs, so a parallelogram is not a trapezoid by that definition.

If you give the slope of EF (or the coordinates or an image), I’ll check each of the five statements and tell you which are true with a brief justification.