InterMath | Workshop Support | Write Up Template
Title
FORMING A SQUARE
Problem Statement
Find four equations whose graphs are oblique (slanted) lines that will intersect to form the
vertices of a square.
What is true about the slopes of the intersecting sides?
What is true about the slopes of the sides opposite of each other?
Problem setup
Create a square by using oblique lines that intersect and form one of the vertices of your
square; compare the slopes of the intersecting sides to see if there is any relationships; after
comparing the slopes of the sides opposite of each other, you will find a relationship.
Plans to Solve/Investigate the Problem
Discuss the properties of a square. Provide examples of polygons and ask students would the
polygons be squares. Have them provide explanations for their answers. Define oblique,
intersecting, and opposite sides. Ask for terms that would possibly describe intersecting and
opposite sides ( perpendicular, parallel). Have students go to the graph on their Geometer’s
Sketchpad and practice creating a few lines. Then let them experiment with attempting to make
a square for a few minutes.
Investigation/Exploration of the Problem
Have students open the Geometer’s Sketchpad to the graph. Have them draw a line on the
graph. Then using the segment icon, draw a segment on the line that was drawn. Hide the line.
Only the segment will be visible. Highlight the endpoints and segment. While these are
highlighted, double click on one endpoint so the bulls eye appears. Go to “transform”, then
rotate. You will have half of a square. The new segment that was create should then be
highlighted as well as its endpoints; double click on the endpoint not connected to the first side
until the bulls eye appears. Again go to “transform”, then “rotate. The third side of the square
will appear. Repeat the process to get the fourth side.
Now you want to get the equation and slope for the line; however it will not work since you
don’t have any lines. So you need to go back now and make the sides of the square into lines.
Do this by highlighting each segment, going to “Construct,” and selecting “Line.”
Once you have lines, you can get the slope and equation by selecting “Measure,” then
equation, then going back to “Measure” and selecting “slope.” ONE IMPORTANT THING TO
REMEMBER IS TO SELECT AN AREA ON YOUR LINE THAT IS OUTSIDE THE
SQUARE. IT WILL NOT WORK IF YOU SELECT ON THE LINE THAT MAKES UP PART
OF THE SQUARE.
8
6
KJ: y = 0.50x+5.03
Sl ope KJ = 0.50
4
J
KJ': y = -2.00x-14.90
2
Sl ope KJ' = -2.00
K
-10
-5
5
-2
10
K'
JK': y = -2.00x+0.00
-4
Sl ope JK' = -2.00
J'
K'J': y = 0.50x-2.42
-6
Sl ope K'J' = 0.50
-8
Students should be able identify the perpendicular lines and the parallel lines. Comparing the
equations and slopes the lines, we find the slopes of the perpendicular lines are opposite
reciprocals. In the diagram above the slope for line KJ is negative two. The opposite reciprocal
is positive .50. The slopes of the sides opposite of each other are the same.
Extensions of the Problem
Using properties of other polygons, students could attempt to graph lines creating the
polygons. Using their create polygons, they could look for possible lines of symmetry. They
could also attempt to create three dimensional figures. Students could also work algebraic
problems and then graph lines.
Author & Contact
Barbara Rodgers
Insert Email
Link(s) to resources, references, lesson plans, and/or other materials
Link 1
Link 2
Important Note: You should compose your write-up targeting an audience in mind rather
than just the instructor for the course. You are creating a page to publish it on the web.