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Chapter Five: |
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Geometry Notes Chapter 5 Section 5.1
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Take notes on the following topics.
Vocabulary Concurrent lines (p. 257) Concurrent lines are three or more lines that meet in one point. The point at which they meet is the point of concurrency. Circumcenter (p. 257) A circumcenter is the point of concurrency of the perpendicular bisectors of a triangle. Circumscribed about (p. 257) A circle is circumscribed about a polygon if the vertices of the polygon are on the circle. A polygon is circumscribed about a circle if all the sides of the polygon are tangent to the circle. Incenter of a triangle (p. 257) An incenter of a triangle is the point of concurrency of the angle bisectors of the triangle. Inscribed in (p. 257) A circle is inscribed in a polygon if the sides of the polygon are tangent to the circle. A polygon is inscribed in a circle if the vertices of the polygon are on the circle. Median of a triangle (p. 258) A median of a triangle is a segment that has as its endpoints a vertex of the triangle and the midpoint of the opposite side. Centroid (p. 258) The centroid of a triangle is the point of intersection of all the lines that contain the medians of that triangle. Altitude of a triangle (p. 259) An altitude of a triangle is a perpendicular segment from a vertex to the line containing the side opposite that vertex. Orthocenter (p. 259) The orthocenter of a triangle is the point of intersection of the lines containing the altitudes of the triangle.
Theorem 5-6 The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices Theorem 5-7 The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides Theorem 5-8 The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. Theorem 5-9 The lines that contain the altitudes of a triangle are concurrent |
