Page 179 - IM_FL_Geometry_Print Sample

1. Where should they build the airport if they want it to be the same distance from each town center? Describe how to nd the precise location.
2. Where should they build the airport if they want it to be the same distance from each of the roads connecting the towns? Describe how to nd the precise location.
Student Response
1. They should build the airport at the circumcenter of triangle . This can be found by locating the intersection of two perpendicular bisectors of the sides of the triangle.
2. They should build the airport at the incenter of triangle . This can be found by locating the intersection of two angle bisectors of angles of the triangle.
Student Lesson Summary
We saw before that the incenter is located at a point that is the same distance from all 3 sides of a triangle. Is there a point that is the same distance from all 3 vertices of a triangle? Yes! The key fact we need is that the perpendicular bisector is exactly those points that are the same distance from the endpoints of a segment.
So if we want a point that is the same distance from vertices and it needs to be on the perpendicular bisector of . If the point is also on the perpendicular bisector of it will be
the same distance from and . This means that intersection point, is the same distance from all 3 vertices. That means must also lie on the perpendicular bisector of
. This common intersection of all 3 perpendicular bisectors of the sides is called the circumcenter of the triangle.
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Teacher Guide