Question

Hiep is writing a coordinate proof to show that the midsegment of a trapezoid is parallel to its bases. He starts by assigning coordinates as given, where RS¯¯¯¯¯ is the midsegment of trapezoid KLMN. Which statement is correct about the midsegment of a trapezoid?

A. The midsegment is not parallel to the bases.
B. The midsegment is parallel to one of the bases.
C. The midsegment is parallel to both bases.
D. The midsegment is always shorter than the bases.

Answer 1

The midsegment of a trapezoid is parallel to both bases.

Step-by-step explanation:

The statement that is correct about the midsegment of a trapezoid is C. The midsegment is parallel to both bases.

A midsegment of a trapezoid is a line segment that connects the midpoints of the legs of the trapezoid. In this case, RS is the midsegment of trapezoid KLMN.

Since RS connects the midpoints of KL and MN, it is parallel to both bases KL and MN. This can be proved using coordinate geometry by assigning coordinates to the vertices of the trapezoid and showing that the slopes of RS and the bases are equal.