Exploring Quadrilaterals Geometers Sketchpad Activity
Quad 1
1) Use the “Segment Tool”
to construct a quadrilateral similar to the one shown below.
2) Measure all of the interior angles by doing the following:
a) Click the “Select Tool”
b) Make sure nothing is currently selected by clicking on empty space on the sketchpad
c) Select three points of each angle in order so that the vertex point is selected in the middle
d) Click the “Measure” drop down menu and select “Angle”
e) Repeat for all four interior angles
3) Sum the angles of the quadrilateral:
a) Click the “Measure” drop down menu and select “Calculate”
b) Sum the angle measures and press “OK”
4) Use the “Text Tool”
to conclude what you discovered about the sum of the angles, and why you know your
discovery to be true (you may have to double-click before you can start typing).
Quad 2
1) Construct two segments that share an endpoint by doing the following:
a) Use the “Segment Tool” to construct the segment AB .
b) Use the “Segment Tool” again to construct segment BC by first clicking on point B. Make this segment
slightly longer than AB
2) Create two parallel lines by doing the following:
a) Click the “Select Tool” and click empty space
b) Select the segment AB and the point C.
c) Click the “Construct” drop down menu and select “Parallel Line”
d) Click empty space, then select the segment BC and the point A
g) Click the “Construct” drop down menu and select “Parallel line”
3) Use the “Point Tool”
and place point D at the intersection of the two lines you have constructed
4) Hide the two parallel lines by doing the following
a) Click the “Select Tool”
b) Right-click the line AD and select “Hide Parallel Line”
c) Do the same thing with line CD
5) Use the “Segment Tool” to construct segments AD and CD
6) Measure all of the interior angles as in Quad 1 step #2.
7) Measure the length of each segment by doing the following:
a) Click the “Select Tool”
c) Right click each segment and select “Length”
8) Measure the slope of each segment by doing the following:
a) Click the “Select Tool”
c) Right click each segment and select “Slope”
9) Draw diagonals AC and BD using the “Segment Tool”
10) Using the “Select Tool”, select both diagonals, click “Construct” from the drop down and select “Midpoints”
11) Use the “Text Tool” to answer the following
#1) What type of quadrilateral did you construct?
#2) What do you notice special about the angle measures, and explain why?
#3) What do you notice special about the lengths of the sides, and explain why?
#4) What do you notice special about the slopes of the sides, and explain why?
#5) What do you notice about the midpoints of the diagonals, and explain why?
Quad 3
1) Use the “Circle Tool”
to create a circle by clicking in the center of the sketchpad and dragging to the right
(radius about 2 inches—no bigger).
2) Use the “Point Tool” to create a point C on the circle as shown below
3) Use the “Segment Tool” to connect your points and construct AB and AC
4) Click the “Select Tool” and hide the circle by right-clicking on the circle and selecting “Hide Circle”
5) Create the following parallel lines as in Quad 2 step #2:
a) Parallel to AB through point C.
b) Parallel to AC through point B
3) Use the “Point Tool” and place point D at the intersection of the two lines you have constructed
4) Hide the two parallel lines you created ( BD and CD ) as in Quad 2 step #4
5) Construct segments BD and CD using the “Segment Tool”
6) Construct the diagonal AD
7) Measure the four angles created by the diagonal – mBAD , mCAD , mBDA , mCDA
8) Use the “Select Tool” to drag point B and observe the angle measures as you manipulate the figure.
9) Construct the diagonal BC
10) Measure the slope of each of the two diagonals
11) Click the “Measure” drop down menu and select “Calculate” to find the opposite reciprocal slope of AD
a) Type “-1/ ” and then click on “Slope AD ” on the sketchpad screen and press “OK”
12) Use the “Select Tool” to drag point B and observe the slopes as you manipulate the figure.
13) Use the “Text Tool” to answer the following
#1) What type of special parallelogram did you construct?
#2) What do you notice about what the diagonals did to the angles of the figure? Why?
#3) What special feature do you notice about the slopes of the diagonals? Why is this true?
14) Click “File” then “Save As” and add your last name and period # to the beginning such as “sloop2 exploring
quadrilaterals.gsp” and then drop it into my drop folder.