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Soo Han
1. This activity will help students investigate the stage for the proof that the sum of the interior
angles of a triangle is 180 degrees. Students will use GSP to create parallel lines and a triangle by
the instruction and instructional worksheet and find the relationship these angles.
2. Students would use the sketch activity as following:
1) Students will open GSP icon. They will use the straightedge tool, and then draw a horizontal
line segment. Label its vertices P and Q. They will draw a point below the ling segment PQ.
Label it Y.
2) Students will select the point Y and the segment PQ (not the vertices, just the segment). From
the Construct menu, choose ConstructParallel Line. This should create a line parallel to PQ
through Y.
3) Students will draw a point on your new line to the left of Y, and label it Z.
4) Students will draw a point on PQ and label it X.
5) Students will select the parallel line. From the Display menu, choose DisplayHide Parallel
Line. This should cause the line to vanish. You should still see the segment PQ, its vertices P
and Q, and the points X, Y, and Z.
6) Students will select X Y and Z and from the Construct menu, choose Construct Segments.
This should create the triangle XYZ.
7) Students will save your sketch
8) Students will use a point tool, and click on the angles given on the investigation worksheet.
Then go to Measure. Click on angle.
9) Students will write down the angles that you measure. Click on the segment PQ. The move
the segment and notice the angles.
10) Students will save your sketch.
3. Students can learn by the fact that the sum of the interior angles of a triangle is 180 degrees
instrumentally. However, having students explore themselves using GSP will vastly help them
understand more than knowing the fact and proof. This activity emphasized not only help students
understand the sum of the all interior angles of a triangle is 180 degrees by creating different
triangles and measures the angles, but also help understand the relationship these angles in parallel
line and a triangle. Eventually, they know the proof of sum of interior angles of a triangle is 180
degrees. They will also develop using technology when they use GSP software. Additionally,
students will develop broad mind to develop the relationship between parallel lines and triangles and
other areas in Geometry. Hopefully, some students develop more visual understanding Geometry
while using GSP.
4. This is a great opportunity for students to learn and use the technology in order to learn the proof
instead of only observing the facts of proof. If the school provides enough computers for number of
students in my class, that would be ideal for this lesson, but if there were not enough computers for
students to investigate, then I have two things in my mind. One is that I can show it through the
projector connected to the computer that every student can watch what happen and do the worksheet
together as a whole class. The other is I will make up of groups of students and they as a group will
come to the computer station and do the work as a group. So that everybody get to see and discuss
what happens and understand the relationship these angles. After all, students will use he GSP
sketching instruction and do the investigation worksheet.
GSP Activity: Parallel Lines and Triangles
Sketching Instructions
1. Using the straightedge tool, draw a horizontal line segment. Label its vertices P and Q.
2. Using the point tool, draw a point below the line segment PQ. Label it Y.
3. Select the point Y and the segment PQ (not the vertices, just the segment). From the Construct
menu, choose ConstructParallel Line. This should create a line parallel to PQ through Y.
4. Draw a point on your new line to the left of Y, and label it Z.
X
P
5. Draw a point on PQ and label it X.
Y
Q
Z
6. Select the parallel line. From the Display menu, choose DisplayHide Parallel Line. This
should cause the line to vanish. You should still see the segment PQ, its vertices P and Q, and the
points X, Y, and Z.
7. Select X Y and Z and from the Construct menu, choose Construct Segments. This should
create the triangle XYZ.
8. Save your sketch
X
P
Y
Q
Z
Name _________________________
GSP Activity: Parallel Lines and Triangles
Investigation Worksheet
1. Measure the angles inside the triangle YXZ, XZY, ZYX.
Next measure the other angles along PQ, PXY, ZXQ (you
already have YXZ).
X
P
Y
Q
Z
2. Drag the points around and observe how the values of the angles change. Record these angles for
three (3) different triangles in the table below.
Angles along PQ
Angles in Triangle
Triangle ZYX.
XZY
YXZ
PXY
ZXQ
1
2
3
3. Write an algebraic expression that relates the angles inside the triangle to each other.
__________________________________________________
4. Write an algebraic expression that relates the angles along PQ to each other
______________________________________________
5. Which angles inside the triangle are equal to which angles along PQ?
__________ is equal to __________
__________ is equal to __________
6. In the diagram below, indicate which angles are equal to each other (use  and  to show which
angles are equal).
P
X
>
>
Y
>
>
Q
Z