Page 181 - IM_FL_Geometry_Print Sample

Lesson 10 Practice Problems
Problem Statement
Point lies on the angle bisector of angle . Point lies on the perpendicular
bisector of side .
a. What can we say about the distance between point and the sides and vertices of triangle ?
b. What can we say about the distance between point and the sides and vertices of triangle ?
Solution
a. Sample response: Point is the same distance to side and . It is closer to point than it is to point .
b. Sample response: Point is the same distance to point as it is to point . It is closer to side than it is to side .
Problem Statement
Noah says, “Here’s 2 perpendicular bisectors of a triangle. That means the point where they intersect is the circumcenter!” Lin responds, “No, we still need to check the third perpendicular bisector to make sure it intersects at the same point.” Do you need 3, or is 2 enough? Explain your reasoning.
Solution
Sample response: Noah is correct that we only need two perpendicular bisectors, because a point that is equidistant to vertices 1 and 2 and equidistant to vertices 2 and 3 is equidistant to all three vertices. Lin’s idea of checking the third perpendicular bisector is not necessary, but it could help catch some computational errors.
Problem Statement
The angles of triangle measure 30 degrees, 40 degrees, and 110 degrees. Will its circumcenter fall inside the triangle, on the triangle, or outside the triangle? Explain your reasoning.
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