Chapter 10 Quiz

Chapter 10 Quiz

1. 10.3

   • Theorem 10-1
     • Theorem 10-1: Bisectors of the angles of a triangle intersect in a point that is equidistant from the three sides of a triangle.
   • Theorem 10-2
     • Perpendicular bisectors of the sides of a triangle intersect in a point that is equidistant to all the vertices.
   • Theorem 10-3
     • Altitudes all meet at point.
   • Theorem 10-4
     • The medians of a triangle intersect in a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.

2. 10.7

   • Drawing a locus that satisfies one condition
     • A locus in a plane is a set of all points in a plane that satisfy a given condition or set of given condition. Locus is derived from the Latin Word for “location.” The plural of locus is loci, pronounced “low-sigh.”
     • A locus is often described as the path of an object moving in a plane. For instance, the reason many clock surfaces are circular is that the locus of the end of a clock’s minute hand is a circle.
   • Finding a Locus
     • To find the locus of points that satisfy a given condition, use the following steps: Draw any figures that are given in the statement of the problem. Locate several points that satisfy the given condition. Continue drawing points until you recognize the pattern. Draw the locus and describe it in words.
   • Drawing loci that satisfy two or more conditions
     • To find the locus of points that satisfy two or more conditions, first find the locus of points that satisfy each condition alone. Then find the intersection of these loci.