1. Do Now 1. For A(–4, 8) and B(5, 8), find the midpoint of AB.
ANSWER 1 2
, 8
2. For A(–3, 2) and B(4, –1), find the length of AB.
ANSWER 58
3. For A(0, 4) and C(18, 4), find the length of AB, where B is a point the distance from A to C. 2 3
ANSWER 12

2. 5.4: Medians and Altitudes
Geometry
5.4: Medians and Altitudes

3. Median
Segment from a vertex to the midpoint of the opposite side is a median.
Example: AC is a median of triangle ABD and
XW is a median of triangle XYZ.
A X
B C D Y W Z

4. Altitude Perpendicular segment from vertex to opposite side.
Acute triangles- altitude is inside the triangle.
Obtuse- altitude is outside.
Right- altitude is on the triangle.

5. Altitude
Example: PQ is an altitude of acute triangle PRS, LM is an altitude of obtuse triangle LNO, and XY is an altitude of right triangle XYZ. P
L X
N O M
R Q S
Y Z

6. Concurrency of Medians of a Triangle
The medians of triangle ABC meet
at point P.
P is called the centroid because it is where the three medians of a triangle intersect.
Y Z P
A B X

7. Concurrency of Medians of a Triangle
AP = AZ
CP = CX
BP = BY OR
2PX = CP
2PY = BP
2PZ = AP C
Y Z P
A B X

8. Concurrency of Altitudes of a Triangle
The altitudes of triangle ABC meet at point P.
P is called the orthocenter because it is where the three altitudes of a triangle intersect. Y Z P
A B X

9. Concurrency of Altitudes of a Triangle
Acute triangle:
orthocenter inside triangle.
Obtuse triangle:
orthocenter outside triangle.
Right triangle:
orthocenter on
side of triangle. Y Z P
A B X

10. Examples

11. Examples

12. Examples

13. Examples

14. Examples

15. Homework
Worksheet 5.4 B – OMIT #7,8,9,25,26