Name _______________________________________ Date _______________ Period _______
GEOMETRY
TRIANGLE PROPERTIES
TEXAS GOES
GREEN
While visiting the capital building in Austin on your school field trip, you overhear two
congressmen talking about creating a new wind farm that is centrally located between Amarillo,
Dallas and San Antonio. They discuss how business will grow around this new wind farm and
how land values will soar. You have decided to take the savings that your grandparents gave you
and buy some property at this new location. The problem is WHERE IS THIS LOCATION?
1. Before doing any work, form a hypothesis about where you think the wind farm will be.
Using a tack, mark it on the map at the front of the room.
2. Using the Patty Paper, complete the 4 methods below to find the ‘center’ of the triangle.
Method 1: The Centroid
- Place the Patty Paper over your map and, using a ruler, trace the triangle formed by
the cities of Amarillo, Dallas and San Antonio.
- Fold your Patty Paper to find the midpoint of each side.
- Connect the midpoint of each side to the opposite angle.
Q: What is the line that connects the midpoint to the opposite angle called?
-
Place a point where the three lines intersect and label it ‘centroid’.
Method 2: The Circumcenter
- Place the Patty Paper over your map and, using a ruler, trace the triangle formed by
the cities of Amarillo, Dallas and San Antonio.
- Fold your Patty Paper to find the midpoint of each side.
- Draw a perpendicular line through the midpoint.
Q: What is this line called?
-
Place a point where the three lines intersect and label it ‘circumcenter’.
Method 3: The Incenter
- Place the Patty Paper over your map and, using a ruler, trace the triangle formed by
the cities of Amarillo, Dallas and San Antonio.
- Fold your Patty Paper to form the angle bisectors for each of the 3 angles.
- Place a point where the three lines meet and label it ‘incenter’.
Method 4: The Orthocenter
- Place the Patty Paper over your map and, using a ruler, trace the triangle formed by
the cities of Amarillo, Dallas and San Antonio.
- Fold your Patty Paper to form the altitude of each side.
Q: How did you form the altitude for each side? Explain in a complete sentence.
-
Place a point where the three lines intersect and label it ‘orthocenter’.
3. Comparing the 4 methods used to find the ‘center’ for the new wind farm, which to you
think is most likely and why?
4. What other factors might the congressmen take into account when determining the
location?