Question

Consider quadrilateral EFGH.

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

EH is parallel to FG and EFGH is a trapezoid because it has exactly one pair of parallel opposite sides.

Step-by-step explanation:

To determine which statements are true, let's first analyze the information given. We are told that the slope of EF is a straight line with positive slope. From this information, we can deduce the following:

1. EH is parallel to FG: Since EF and GH are opposite sides of the quadrilateral, if EF is parallel to GH, then EH must be parallel to FG.

2. EF is perpendicular to EH: Since the slope of EF is positive, it cannot be perpendicular to EH.

3. HG is neither parallel nor perpendicular to FG: Since EH is parallel to FG, HG cannot be parallel or perpendicular to FG.

4. Quadrilateral EFGH is a rectangle because it is a parallelogram with four right angles: We do not have enough information to determine if EFGH is a rectangle. Having four right angles is a characteristic of rectangles, but we cannot determine this solely based on the given information.

5. Quadrilateral EFGH is a trapezoid because it has exactly one pair of parallel opposite sides: Since EH is parallel to FG, and EF and GH are opposite sides of the quadrilateral, it has exactly one pair of parallel opposite sides, making it a trapezoid.

Answer 2

B and C

Step-by-step explanation: