The figure below shows a partially completed set of steps to construct parallelogram PQRS: Two sides of a parallelogram PQRS are

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The figure below shows a partially completed set of steps to construct parallelogram PQRS: Two sides of a parallelogram PQRS are

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 parallelogram so that side RS is congruent to side PQ. The chart below 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

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-03-27T11:18:52+03:00

Response:

∠PQL=∠TRN [Angles corresponding]

Thus, PQ║RS and PQ=RS

Detailed explanation:

The side PQ has been drawn.

A second side QR is traced, forming an acute angle with side PQ.

Now side QR is extended to the left.

Create an arc from point Q such that it intersects QP at M and extends RQ at L. Without altering the compass width (i.e., the distance between the nib and pencil), draw an arc from R to intersect RQ at N. Now measure the distance LM with a compass. Position the compass at N and mark an arc cut from point R. Designate this intersection as T. Draw a line from point R through T. Then measure the length of PQ with the compass. Position your compass at R and create an arc on the produced line RT at S. Thus, we ascertain that PQ║RS and PQ=RS.

This occurs because

∠MQL=∠NRT [corresponding angles, with QR acting as the transversal]

∵PQ║RS and PQ=RS [This identifies PQRS as a parallelogram]

Out of the four students who illustrated their explanations

Student 2 presented a partially correct but valid explanation.