Medians and Altitudes

1
Medians and Altitudes

• Median A segment whose endpoints are a vertex
  of a triangle and the midpoint of the side
  opposite the vertex.
• Centroid The point of concurrency for the
  medians of a triangle.
• Centroid Theorem
• The centroid of a triangle is located two thirds
  of the distance from a vertex to the midpoint of
  the side opposite the vertex on a median.

2
Example 1-2a
3
Example 1-2a
Find a.
Segment Addition Postulate
Centroid Theorem
Substitution
Multiply each side by 3 and simplify.
Subtract 14.8 from each side.
Divide each side by 4.
4
Example 1-2a
Find b.
Segment Addition Postulate
Centroid Theorem
Substitution
Multiply each side by 3 and simplify.
Subtract 6b from each side.
Subtract 6 from each side.
Divide each side by 3.
5
Example 1-2a
Find c.
Segment Addition Postulate
Centroid Theorem
Substitution
Multiply each side by 3 and simplify.
Subtract 30.4 from each side.
Divide each side by 10.
Answer
6
Example 1-2b
7
Medians and Altitudes

• Altitude - A segment from a vertex to the line
  containing the opposite side and perpendicular to
  the line containing that side.
• Orthocenter The point of concurrency of the
  altitudes of a triangle.