Question

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

Answer 1

2

Explanation:

Answer 2

∠PQL=∠TRN [Corresponding angles]

So, PQ║RS and PQ=RS

Explanation:

Side PQ is drawn.

Another side QR is drawn making an acute angle with side PQ.

Now side QR is extended towards left.

Draw an arc from point Q such that it cuts QP at M and RQ produced at L. Without changing the compass width i.e distance between nib and pencil draw an arc from point R such it cuts RQ at N.Now measure the Distance LM using compass.Place the compass at N and cut an arc that you have drawn from point R.Mark this pont as T.Draw a line passing from R and T .Then measure the length of PQ using compass.Put your compass at R and cut an arc on the line RT produced at S.Then the line PQ ║RS and PQ =RS.

Why this happens because

∠ MQL=∠NRT [ corresponding angles taking QR as Transversal]

∵PQ║RS and PQ=RS [PQRS is a parallelogrm]

Out of four students who has written the explanation

Student 2 has written not fully but correct explanation.