Constructing Quadrilaterals
Using Geometer’s Sketch Pad
Save this Sketch as “Quadrilaterals”
Note: It will have 6 pages
1.
Trapezoid: A quadrilateral that contains one pair of parallel sides.
a. Construct a pair of parallel lines.
b. Hide all the original points.
c. Construct 4 more points, 2 on each line.
d. Hide the lines.
e. Highlight all 4 points and construct the segments.
f. Use the text tool to name your construction.
NOTE: You can move any or all of the points and the parallel segments stay parallel. Don’t let the
points “cross over!”
MEASURE ALL THE ANGLES AND TOTAL THEM WITH THE CALCULATOR!
2.
Right Trapezoid: A quadrilateral that contains one pair of parallel sides
and two right angles.
a. Insert a NEW page (File, Document Options).
b. Construct a pair of horizontal, parallel lines.
c. Hide all the original points.
d. Construct 1 point on one of the lines.
e. Highlight the point and its line.
f. Construct a perpendicular line.
g. Construct the intersection that was formed.
h. Now, on either side of the perpendicular line, construct 2 points on the horizontal lines,
1 on one line and 1 on the other.
i.
Hide all three lines.
j.
Highlight the remaining 4 points and construct segments.
k. Use the text tool to name your construction.
NOTE: You should be able to move any of the points or sides and it should ALWAYS have ONE right
angle and ONE pair of parallel sides. Don’t let the points “cross over!”
MEASURE ALL THE ANGLES AND TOTAL THEM WITH THE CALCULATOR!
3.
Parallelogram: A quadrilateral that contains TWO pairs of parallel
sides.
a. Insert a NEW page (File, Document Options).
b. Construct a pair of horizontal, parallel lines.
c. Hide all the original points.
d. Use the straightedge tool to draw a line that crosses both of the parallel lines.
e. Hide both of the line’s original points.
f. Construct both intersections that were formed.
g. Now, on either side of the intersecting line, construct ONE point either one of the
horizontal lines.
h. Highlight that point and the intersecting line.
i.
Construct a parallel line.
j.
Construct the intersection that was formed.
k. Now, hide all 4 lines.
l.
Highlight all four points and construct the segments.
m. Use the text tool to name your construction.
NOTE: You should be able to move any of the points or sides and it should ALWAYS have TWO
pairs of parallel sides.
MEASURE ALL THE ANGLES AND TOTAL THEM WITH THE CALCULATOR!
4.
Rectangle: A parallelogram with 4 right angles.
a. Insert a NEW page (File, Document Options).
b. Construct a pair of horizontal, parallel lines.
c. Using any one of the three points, construct another line perpendicular to the parallel
lines.
d. Construct the newly formed intersection.
e. Use any point on the original pair of horizontal, parallel lines to construct another line
parallel to the one you just constructed.
f. You now have 2 pairs of parallel lines that are perpendicular to each other.
g. Construct the newly formed intersection.
h. Do you see a rectangle? Highlight all four points and construct the segments.
i.
Hide all other objects.
j.
Use the text tool to name your construction.
NOTE: You should be able to move any of the points or sides and it should ALWAYS have TWO pairs of
parallel sides AND four RIGHT ANGLES!
MEASURE ALL THE ANGLES AND TOTAL THEM WITH THE CALCULATOR!
5.
Rhombus: A parallelogram with all congruent sides.
a. Insert a NEW page (File, Document Options).
WARNING: these directions are tough to follow… read carefully and PERSEVERE!
b. Construct a pair of horizontal, parallel lines.
c. On the line with ONLY one point, highlight the point.
d. Then, highlight ONE of the points on the other line, and construct a Circle by Center +
Point.
e. Highlight the same two points and construct a segment.
f. The circle intersects the line, with ONLY one point, in 2 places. Highlight that line and
the circle and construct those intersections.
g. Choose either intersection and highlight the point, then highlight the segment and
construct a parallel line.
h. Now, construct the newly formed intersection.
i.
Do you see the four points (vertices or corners) of the rhombus? Highlight them and
construct the segments for the rhombus.
j.
Highlight everything else and hide it.
k. Measure and label ALL SIDE LENGTHS!
l.
Use the text tool to name your construction.
NOTE: You should be able to move any of the points or sides and it should ALWAYS have TWO pairs of
parallel sides AND ALL CONGRUENT SIDES!
MEASURE ALL THE ANGLES AND TOTAL THEM WITH THE CALCULATOR!
6. Square: A parallelogram with ALL congruent sides and ALL congruent
Angles
a. Insert a NEW page (File, Document Options).
b. Construct a circle.
c. Double click on the center point to “Mark” it.
d. Highlight the point on the circumference.
e. On the Transform menu, select Rotate, 90 degrees.
f. Rotate it again, 2 more times so that you have 4 equidistant points on the circumference
of the circle.
g. Highlight all 4 points and construct segments.
h. Hide all other objects.
i.
Measure and label ALL SIDE LENGTHS!
j.
Use the text tool to name your construction.
NOTE: You should be able to move any of the points or sides and it should ALWAYS have TWO pairs of
parallel sides AND ALL CONGRUENT SIDES!
MEASURE ALL THE ANGLES AND TOTAL THEM WITH THE CALCULATOR!