# geometry

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

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 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.

Which student used the correct steps to construct parallelogram PQRS?

Student 2

Student 1

Student 4

Student 3

• geometry -

why don't you try getting out your compass, following each of the student's steps, and see which one yields a parallelogram PQRS?

• geometry -

student 1

• geometry -

Student 4

• geometry -

studdent 3

• geometry -

Student 2

• geometry -

Student 1

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