Question

The figure below shows a partially completed set of steps to construct figure 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 and intersects QR extended at N.

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 below 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.

Answer 1

Student 2

Explanation:

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Answer 2

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.

Explanation:

A parallelogram is a two dimensional quadrilateral that has two opposite sides to be equal and parallel. The sum of its internal angles is
`360^(0)`.

Given; parallelogram PQRS

<PQR = <SRN = acute angle

QP = RS

QR = PS

The next step involve locating point S to complete the diagram. To locate point S and complete the figure, the procedure of student 2 would give appropriate location and accurate dimensions.