Geometry Section 5.4

1
GeometrySection 5.4

• Use Medians and Altitudes

2
Median of a Triangle

• A segment from the vertex to the midpoint of the
  opposite side.
• The point of concurrency is the centroid

3
Concurrency of Medians of a Triangle

• The medians of a triangle intersect at a point
  that is two thirds of the distance from each
  vertex to the midpoint of the opposite side.

4
Altitude of a Triangle

• The perpendicular segment from a vertex to the
  opposite side or to the line that contains the
  opposite side.

5
Altitudes in Obtuse Triangles

• Two of the altitudes are on the exterior of the
  triangle

6
Concurrency of Altitudes of a Triangle

• The lines containing the altitudes of a triangle
  are concurrent.
• The point of concurrency is called the orthocenter

7
Orthocenter of an Acute Triangle

• Orthocenter is inside the triangle

8
Orthocenter of an Obtuse Triangle

• Orthocenter of an obtuse triangle is outside the
  triangle

9
Orthocenter of a Right Triangle

• Orthocenter of a right triangle is on the triangle

10
Isosceles Triangle

• In an isosceles triangle, the perpendicular
  bisector, angle bisector, median, and altitude
  from the vertex angle to the base are the same
  segment.

11
Equilateral Triangle

• In an equilateral triangle, the perpendicular
  bisector, angle bisector, median, and altitude
  are the same segment

12
Examples

• classzone

13
Assignment

• Section 5.4
• Page 322
• Problems 4-10 even, 14, 18-22 even, 26
• WEB ON ALTITUDE
• WEB ON MEDIAN