The figure below shows a partially completed set of steps to construct a rhombus PQRS:The next step is to construct side PS of the figure so that side PS is parallel and congruent to side QR. The chart below shows the steps each of the four students took to draw side PS:Student 1 Fix the compass at M and adjust its width to point L. Without changing the width of the compass, move the compass to N and draw a small arc on the big arc. Label the point of intersection of the two arcs as T. Draw a line segment from P that passes through T. Adjust the width of the compass to QR and draw an arc from point P to intersect line PT at S.Student 2 Fix the compass at M and draw an arc that intersects side QP at point T. Without changing the width of the compass, move the compass to R and draw an arc. Adjust the width of the compass to QR and draw an arc from point P. Draw a line segment from R that passes through T and intersects the second arc at S.Student 3 Fix the compass at L and adjust its width to point M. Without changing the width of the compass, move the compass to R and draw an arc which intersects QR at point T. Draw a line segment from R that passes through T and intersects the arc at S.Student 4 Fix the compass at L and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc which intersects QR at point T. Draw a line segment from R that passes through T and intersects the arc at S.Which student used the correct steps to construct rhombus PQRS?A. Student 2B. Student 4C. Student 3D. Student 1
Accepted Solution
A:
student 1 was correct. When compass is placed at M and width is adjusted to L, that distance between M and L corresponds to the angle ∠LQM. Therefore the distance between L and M should be equal to the distance between N and point T which is to be constructed. IF the distance LM = NT then the angles ∠LQM and ∠NPT are equal . these are corresponding angles which means that PT and QR are parallel. PT straight segment is extended. Since opposite sides in a rhombus should be equal, the compass width is adjusted to QR and compass is placed on P to mark the distance of where point S will line on the extended PT line. This is so that PS = QR. hence, a line PS is drawn that is parallel to QR and equal in length