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Honors Geometry

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Goal 1: How to identify special segments in a triangle ... bisector of a triangle is a segment that ... Their common point is the circumcenter of the triangle. ... – PowerPoint PPT presentation

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Title: Honors Geometry


1
Honors Geometry
  • Lesson 5.2
  • Special Segments in a Triangle
  • Geometry Applet

2
What You Should LearnWhy You Should Learn It
  • Goal 1 How to identify special segments in a
    triangle
  • Goal 2 How to use properties of special segments
    to solve problems in geometry and in real life
  • Using the properties of special segments related
    to triangles can help you answer questions about
    triangular objects, such as how to find the
    balancing point of a triangular model

3
Perpendicular Bisector of a Triangle
  • A perpendicular bisector of a triangle is a
    segment that is part of a perpendicular bisector
    of one of the sides
  • It lies in the triangles interior
  • The endpoints are points of the triangle
  • May or may not have a vertex as one endpoint

4
Angle Bisector of a Triangle
  • An angle bisector of a triangle is a segment that
    bisects one of the angles of the triangle
  • It lies in the triangles interior
  • The endpoints are points of the triangle
  • A vertex is one of the endpoints

5
Median of a Triangle
  • A median is a segment whose endpoints are a
    vertex and the midpoint of the opposite side
  • It lies in the triangles interior
  • The endpoints are points of the triangle
  • A vertex is one of the endpoints

6
Altitude of a Triangle
  • An altitude is a segment from a vertex that is
    perpendicular to the opposite side or to the line
    containing the opposite side
  • An altitude may lie inside or outside the
    triangle
  • A vertex is one of the endpoints

7
Lesson Investigation
8
Using Concurrency Properties
  • Every triangle has three perpendicular bisectors,
    three angle bisectors, three medians, and three
    altitudes

9
Theorem 5.5Concurrency Properties (circumcenter)
  • The lines containing the perpendicular bisectors
    of a triangle are concurrent (meeting in one
    point).
  • Their common point is the circumcenter of the
    triangle.
  • The circumcenter is equidistant from the vertices
    of the triangle

10
Theorem 5.5Concurrency Properties (incenter)
  • The angle bisectors of a triangle are concurrent.
  • Their common point is the incenter of the
    triangle.
  • The incenter is equidistant from the three sides
    of the triangle

11
Theorem 5.5Concurrency Properties (centroid)
  • The medians of a triangle are concurrent.
  • Their common point is the centroid of the
    triangle
  • The centroid is ? of the distance from each
    vertex to the midpoint of the opposite side

12
Theorem 5.5Concurrency Properties (Orthocenter)
  • The lines containing the altitudes of a triangle
    are concurrent
  • Their common point is the orthocenter of the
    triangle

13
Find the balancing point of a triangular model
14
THE END
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