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Title CAPTURE THE FLAG

Problem Statement

Three teams, A, B, and C, each start from a vertex of a scalene triangular field. Their goal is to be the first team to grab the flag that is located inside the triangular field. If the game is fair, then each team has to run the same distance to get to the flag.

Where should the flag be positioned for the game to be fair? Describe how you found the position.

Problem setup Different starting points for 3 teams would be how far from the flag they need to win the game if the teams are playing on a triangular field?

Plans to Solve/Investigate the Problem First I would have a square shape, rectangular shape, and triangular shape and have students place markers where the three teams ought to start and the flag ought to be and let them measure to check to see if their placements were right. Discuss why it might be easier to arrange the game on a square or rectangular field instead of a triangular area. On the Geometer’s Sketchpad the students would need to build a triangle, preferably a scalene triangle. Next construct perpendicular bisectors. Make sure this is done for each of the three sides. The point of intersection (also known as the circumcenter) is where all three lines converge or meet. Construct segments from the circumcenter to each vertex of the original triangle. Repeat these steps for the other two segments. Once the segments have been drawn, measure them to prove the circumcenter is where the flag should be place. Investigation/Exploration of the Problem First I would have a square shape, rectangular shape, and triangular shape and have students place markers where the three teams ought to start and the flag ought to be and let them measure to check to see if their placements were right. Discuss why it might be easier to arrange the game on a square or rectangular field instead of a triangular area. On the Geometer’s Sketchpad the students would need to build a triangle, preferably a scalene triangle. To do this, click on the point icon and make 3 points on the screen. Select all the points; go to “construct” and then “segments.” Next construct perpendicular bisectors. To do this, locate the midpoint of each segment by highlighting the segment, then clicking on “construct” and “midpoint.” Once the midpoint has been established, highlight the midpoint and the side, go to “construct” then “ perpendicular lines.” Make sure this is done for each of the three sides. The point of intersection (also known as the circumcenter) is where all three lines converge or meet.

Construct segments from the circumcenter to each vertex of the original triangle. Do this by placing a point at the circumcenter. Highlight this point and the point of the first vertex; once both points are highlighted, go to “construct” then segment.” To make it more visible and less confusing go to “display” and “color” and make this segment a different and bright color from the other markings. Repeat these steps for the other two segments. Once the segments have been drawn, measure them. Highlight the segment and then go to “measure” and “length.” All three segments should measure the same length, proving that the circumcenter is where the flag should be placed. m EF = 6.87 cm m EG = 6.87 cm m EH = 6.87 cm

Extensions of the Problem Once the segments have been measured and discovered to be the same, click on the circle icon. Start at the circumcenter and drag the circle out until it reaches all the corners of the original vertexes. Seeing the vertexes are all evenly on the circle may help to understand the distance is the same. m EF = 6.87 cm m EG = 6.87 cm m EH = 6.87 cm

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.