EMAT 6700

Rectangle

Use geometer's sketchpad to construct a rectangle.

Construct a rectangle with the measure of segment LM as the length and the measure of segment WN as the width.

1.  Construct line q and point P on line q.

(Construct segment LM and segment WN on you sketch congruent to the segments shown above.)

2.  Select point P and segment LM.  Construct circle by center and radius.  Label the point of intersection point K (intersection of circle P and line q).

3.  Select circle P.  Hide the circle.  Select point P and line q.  Construct a perpendicular line.  Select point K and line q.  Construct a perpendicular line.

4.  Select point P and  segment WN.  Construct circle by center and radius.  Label the point of intersection point J (intersection of circle P and the perpendicular line).

5.  Select circle P.  Hide the circle.  Select point J and line q.  Construct a parallel line.  Label the point of intersection point R (intersection of the parallel line and the perpendicular line that passes through point K).

6.  Select line q, the parallel line, and both perpendicular lines.  Hide the lines.  Select point P and point J. Construct segment PJ.  Select point J and point R.  Construct segment JR.  Select point R and point K.  Construct point RK.  Select point K and point P.  Construct segment KP.

Quadrilateral PJRK is a parallelogram and all angles are right angles.  Therefore, quadrilateral PJRK is a rectangle.