The figure shows a partially completed set of steps to construct figure PQRS.



The next step is to construct side RS of the figure so that side RS is congruent to side PQ and angle PQR is congruent to angle SRN. The chart shows the steps each of the four students took to draw side RS of the figure.

Student 1 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. Draw a line segment from R that passes through T and intersects the arc at S.
Student 2 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 an arc which cuts the previous arc at T. Adjust the width of the compass equal to PQ. Fix the compass at R and draw an arc. Draw a line segment from R that passes through T and intersects the second arc at S.
Student 3 Fix the compass at Q and adjust its width to point P. Without changing the width of the compass, move the compass to R and draw an arc. Using the same width, fix the compass at N and draw an arc which intersects the previous arc at 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 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 parallelogram PQRS?

Student 2

Student 1

Student 4

Student 3

student 1

Student 1

To determine which student used the correct steps to construct parallelogram PQRS, we need to carefully analyze each student's construction method based on the given instructions.

Student 1 starts by fixing the compass at point L and adjusting its width to point M. Then, without changing the width, the compass is moved to point R and an arc is drawn. Finally, a line segment from R passes through point T and intersects the arc at point S.

Student 2 begins by fixing the compass at point M and adjusting its width to point L, similar to Student 1. Then, without changing the width, the compass is moved to point N and an arc is drawn, intersecting the first arc at point T. Additionally, the width of the compass is adjusted to match line segment PQ. Finally, the compass is fixed at point R and another arc is drawn. A line segment from R passes through point T and intersects the second arc at point S.

Student 3 starts by fixing the compass at point Q and adjusting its width to point P. Then, without changing the width, the compass is moved to point R and an arc is drawn. Using the same width, the compass is fixed at point N and another arc is drawn, intersecting the previous arc at point T. Finally, a line segment from point R passes through point T and intersects the arc at point S.

Student 4 fixes the compass at point L and adjusts its width to point P, which is different from the instructions. Then, without changing the width, the compass is moved to point R and an arc is drawn, intersecting line segment QR at point T. Finally, a line segment from R passes through point T and intersects the arc at point S.

Based on the given instructions, Student 2 followed the correct steps to construct parallelogram PQRS. Therefore, the correct answer is "Student 2".

Student 4

studdent 3

Student 2

why don't you try getting out your compass, following each of the student's steps, and see which one yields a parallelogram PQRS?