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.

Step-by-step explanation:

Given that KLMN is a trapezium.

K has coordinates (0,0), L(2a,0), M(2d,2c) and N(2b,2c)

R is the mid point of KN

Hence coordinates of R will be using mid point formula (x1+x2/2, y1+y2/2)

= (a,c)

Similarly S is mid point of segment LM.

Hence S = (a+d,c)

The slope of SL is = (y2-y1)/(x2-x1) = (a-d)/-c=(d-a)/c

The slope of RS = (c-c)/d =0

The slope of NM = (2c-2c)/(2b-2d) = 0

Since slope of RS = slope of NM

We get RS is parallel to NM

Already NM is parallel to KL because bases of trapezium

Hence RS is parallel to both the bases.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

might be the correct answer will be question number 2