Question

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

The next step is to construct side RS of the parallelogram so that side RS is congruent to side PQ. The chart shows the steps each of the four students took to draw side RS of the parallelogram.

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 Q and draw an arc that intersects side QP. 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 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. 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. 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?

Answer 1

"Student 3" is the one among the following choices given in the question that is actually correct. The correct option among all the options that are given in the question is the third option or the penultimate option. I hope that this is the answer that you were looking for and the answer has actually come to your desired help.

Answer 2

The correct answer is:

Student 3.

Explanation:

Student 3's response was "- 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. Draw a line segment from R that passes through T and intersects the arc at S. "

Since the compass is set to the width of QP, the arc that is drawn from R will be the same distance from R that P is from Q. Using a straightedge to connect R, T and the arc, this side will be parallel to QP. This gives us the third side of our parallelogram.