Objectives

1
Objectives

• To define, draw, and list characteristics of
• Midsegments
• Altitudes
• Perpendicular Bisectors
• Medians

2
Medians of Triangles

• A median of a triangle is a segment whose
  endpoints are a vertex and the midpoint of the
  opposite side.

3
Perpendicular Bisector

• A perpendicular bisector passes through the
  midpoint of a segment at a right angle with that
  segment

4
Altitude of a Triangle

• An altitude is the perpendicular segment from a
  vertex to the line containing the opposite side.

5
Angle Bisector

• An angle bisector connects a vertex to the
  opposite side and cuts the vertex angle into two
  halves.

6
Midsegments of Triangles

• A midsegment of a triangle is a segment
  connecting the midpoints of two sides

7
Triangle Midsegment Theorem

• If a segment joins the midpoints of two sides of
  a triangle, then the segment is parallel to the
  third side, and is half its length.

8
Point of Concurrency Definition

• When three or more lines intersect in one point,
  they are concurrent. The point at which they
  intersect is the point of concurrency.

9
Centroid

• The point of concurrency of the medians of a
  triangle is the centroid. The centroid is also
  called the center of gravity because it is the
  point where a triangular shape will balance.
• The centroid of a triangle is always located
  inside the triangle.

10
Circumcenter (Perpendicular Bisectors)

• The point of concurrency of the perpendicular
  bisectors of a triangle is the circumcenter of
  the triangle. The circumcenter is the center of
  the circle which passes around the outside of the
  triangle and through each vertex.

11
Orthocenter (Altitudes)

• The point of concurrency of the altitudes of a
  triangle is the orthocenter of the triangle.
• The orthocenter is inside the triangle for an
  acute triangle, at the right angle for a right
  triangle, and outside the triangle for an obtuse
  triangle.

12
Incenter (Angle Bisectors)

• The point of concurrency of the angle bisectors
  of a triangle is the incenter of the triangle.
  The incenter is the center of the circle which
  lies inside the triangle and touches all three
  sides of the triangle. The incenter is always
  inside the triangle.

13
For Exploration

• http//www.keymath.com/x19398.xml
• http//www.keymath.com/x23078.xml