1. Use Medians and Altitudes
Geometry Section 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
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13. Assignment Section 5.4 Page 322
Problems #4-10 even, 14, even, 26
WEB ON ALTITUDE
WEB ON MEDIAN