Name: ___________________________________________ Geometry “Real – World” Project Triangle Centers Choose a triangle center (circumcenter, incenter, centroid, orthocenter) and create a scenario/story to describe how you may actually use the center in real life. Triangle Center Requirements Using Google Maps or other Internet mapping websites, pick three locations of interest to you and print a picture of the map with these locations. On the printed map, draw a triangle between the locations you chose. If you are creating fictional locations or using a construction project example, you must include realistic measurements/distances. Develop a storyline, which includes why one of the triangle centers that we have learned in class would be important information to know with reference to your locations. Sketch the construction of the specific triangle center used and show all markings for the segments you needed to draw (perpendicular bisectors, angle bisectors, medians or altitudes depending on which triangle center you chose). You must use a ruler and a protractor! Triangle Center Real-­‐Life Examples Circumcenter: -­‐The owner of an amusement park wants to clean up the park. For every three rides he is going to add a garbage can. To make it easier for people, he uses the circumcenter of three rides to place the garbage cans (equidistant from the three rides). -­‐There is a neighborhood in Seattle called Denny Triangle because of its triangular shape. Imagine that you and two friends live at each vertex of Denny Triangle. You plan on meeting this weekend at a point that is equidistant from each of your homes. By using perpendicular bisectors to find the circumcenter, you will have found that point. Incenter: -­‐Imagine that there are three busy roads that form a triangle. You want to open a store that is equidistant from each road to get as many customers as possible. Finding the incenter would help you find this point because the incenter is equidistant from all sides of a triangle. -­‐A man is installing a new triangular counter top. He wants to put a stove in the incenter of it so that it is easy to access from all sides. He uses the incenter of the counter to place the stove so it is equidistant from all the sides of the counter. Name: ___________________________________________ Centroid: -­‐Imagine that you are a sculptor. You plan to make a new sculpture that will include a triangle balanced on the tip of another triangle. Once you use you the medians to find the centroid, you will have also found the point of balance. -­‐A carpenter is designing a triangular table with one leg. He uses the centroid of the table because it will be the center of gravity where the table will be balanced and the most stable. Orthocenter: -­‐Orthocenter-­‐ Imagine that you still live at a vertex of Denny Triangle. You want to find the shortest distance you must walk to get to the street that is the opposite side of the triangle. Since a straight line is the shortest distance, finding the street that is perpendicular to the opposite would give you the shortest distance. Finding the orthocenter would give the perpendicular line, or altitude, from any vertex. -­‐A man is designing a new shape for hang gliders. The glide itself will be an obtuse triangle, and he uses the orthocenter of the glide, which will be outside the triangle, to make sure the cords descending down from the glide to the rider are an even length, connecting at one point of concurrency. Presentation: -­‐You may mount your project on poster board, create a power-­‐point presentation, or create a “book” (see rubric for what to include). Please include your rubric with your final project. -­‐Each group must present their project to the class with a brief (3-­‐5 min) explanation of their triangle center scenario and their calculations. Name: ___________________________________________ RUBRIC Geometry “Real – World” Project Triangle Centers Project Details: -­‐Mrs. Mathisen signs off on your idea: __________________________________________________ -­‐Projects printed and mounted on poster, PowerPoint, or “book” -­‐All explanations typed for each project -­‐Colorful, neat, organized -­‐Creativity of ideas for each project (don’t use my ideas) -­‐Triangle Center written story (at least 2 paragraphs) ü Where did you go, what did you create, or what is the scenario? ü Why would you want to find the center? ü How did you find the center? (be specific: used the perpendicular bisector, angle bisector, etc.) ü What was your outcome? Was the center useful? -­‐Construction/calculations of triangle center is shown evidenced by the markings on the segments. (I will be checking your measurements for accuracy!) /1 /3 /3 /3 /3 /12 /15 Presentation (3-­‐5 minutes): -­‐Clear explanation of project ideas, good use of vocabulary/knowledge of the material. Final Grade: /5 /45