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 .

trapezoid k l m n on the coordinate plane. the vertices of the trapezoid are k begin ordered pair 0 comma 0 end ordered pair, l begin ordered pair 2a comma 0 end ordered pair, m begin ordered pair 2d comma 2c end ordered pair, and n begin ordered pair 2b comma 2c end ordered pair. segment r s is drawn with point r on segment k n and point s on segment l m.

drag and drop the correct answers to complete the proof.

since rs is the midsegment of trapezoid klmn , the coordinates of r are (b,) and the coordinates of s are (, c).

the slope of kl is .

the slope of rs is 0.

the slope of nm is 0.

the slope of each segment is 0; therefore, the midsegment is parallel to the bases.