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?
student 3
student 4
To determine which student used the correct steps to construct rhombus PQRS, we need to carefully analyze each student's process and compare it to the requirements of a rhombus construction.
A rhombus is a quadrilateral with all sides congruent and opposite sides parallel. In this case, we want to construct side PS so that it is both parallel and congruent to side QR.
Let's go through each student's steps:
Student 1: This student starts by drawing arcs and then drawing a line segment passing through a point of intersection. While this approach does involve constructing a line parallel to QR, it does not guarantee that the segment is congruent to QR. This student's method does not meet the criteria for constructing a rhombus.
Student 2: This student begins by drawing arcs that intersect side QP. However, they then draw a line segment passing through a different point of intersection. Furthermore, the arc they draw from point P does not intersect the line segment at point S. This student's method also does not meet the criteria for constructing a rhombus.
Student 3: This student fixes the compass at an incorrect point (L) and draws an arc intersecting side QR. Then, they draw a line segment passing through the correct point of intersection. However, they fail to ensure that the line segment is congruent to QR. This student's method does not meet the criteria for constructing a rhombus.
Student 4: This student fixes the compass at an incorrect point (L) and draws an arc intersecting QR. Then, they draw a line segment passing through the correct point of intersection. The line segment also intersects the arc at the correct point. However, they fail to adjust the compass width to QR before drawing the arc from point R. This student's method also does not meet the criteria for constructing a rhombus.
After analyzing the steps of each student, none of them correctly constructed side PS of the figure to be parallel and congruent to side QR. Therefore, none of the students used the correct steps to construct rhombus PQRS.