Question

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

Two sides of a parallelogram PQRS is drawn; PQ that makes an acute angle with the horizontal side QR. QR extends to the left and an arc is drawn that cuts this extended line at L and the side QP at M. An arc of the same measure and the same orientation as arc LM is drawn from point R to cut QR at N. Another small arc intersects this arc at T. The position of T is such that a line segment drawn through RT makes the same angle with QR as angle LQM.

The next step is to construct side RS of the parallelogra

Answer 1

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?

Student 3

Student 2

Student 4


Student 1