1. 5.4 – Use Medians and Altitudes

2. Median
Line from the vertex of a triangle to the midpoint of the opposite side

3. In your group, each person draw a different sized triangle
In your group, each person draw a different sized triangle. One should be scalene obtuse, one scalene acute, scalene right, and one isosceles. Then construct the medians of the triangle.

4. C A B
**always inside the triangle

6. 2/3 the distance from each vertex and 1/3 distance from the midpoint
Point of concurrency
Property
centroid
2/3 the distance from each vertex and 1/3 distance from the midpoint

8. Line from the vertex to midpoint of opposite side
Special Segment
Definition
Median
Line from the vertex to midpoint of opposite side

9. Concurrency Property
Definition
2/3 the distance from each vertex and 1/3 distance from the midpoint
Centroid

10. Line from the vertex of a triangle perpendicular to the opposite side
Altitude
Line from the vertex of a triangle perpendicular to the opposite side

11. In your group, each person draw a different sized triangle
In your group, each person draw a different sized triangle. One should be scalene obtuse, one scalene acute, scalene right, and one isosceles. Then construct the altitudes of the triangle.

12. C A B

15. Point of concurrency
Property
orthocenter
none

17. Line from vertex  to the opposite side
Special Segment
Definition
Altitude
Line from vertex  to the opposite side

18. Concurrency Property
Definition
orthocenter
If acute – inside of triangle
If obtuse – outside of triangle
If right – at vertex of right angle

19. Perpendicular Bisector
Circumcenter
Angle Bisector
Incenter
Median
Centroid
Altitude
Orthocenter P C A I M C A O

20. 6

21. In PQR, S is the centroid, PQ = RQ, UQ = 5,
TR = 3, and SU = 2. Find the measure.
Find TP. 3

22. In PQR, S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2
In PQR, S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure.
Find SV. 3 2

23. In PQR, S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2
In PQR, S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure.
Find RU. 3 2
4 + 2 = 6 4

24. In PQR, S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2
In PQR, S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure.
Find ST. 3 3 2 4

25. In PQR, S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2
In PQR, S is the centroid, PQ = RQ, UQ = 5, TR = 3, and SU = 2. Find the measure.
Find VQ. 3 3 2 4 5

26. G In ABC, G is the centroid, AE = 12, DC = 15. Find the measure. B
Find GE and AG.
GE = 4
AG = 8 E D 12 G A C F

27. G In ABC, G is the centroid, AE = 12, DC = 15. Find the measure. B
Find DG and GC.
DG = 5
GC = 10 E D 12 G 15 A C F

28. OL = 5x – 1 and LQ = 4x – 5 5x – 1 = 2(4x – 5) 5x – 1 = 8x – 10
Point L is the centroid for NOM. Use the given information to find the value of x.
OL = 5x – 1 and LQ = 4x – 5
5x – 1
5x – 1 =
2(4x – 5)
4x – 5
5x – 1 = 8x – 10
–1 = 3x – 10
9 = 3x
3 = x

29. LP = 2x + 4 and NP = 9x + 6 3(2x + 4) = 9x + 6 6x + 12 = 9x + 6
Point L is the centroid for NOM. Use the given information to find the value of x.
LP = 2x + 4 and NP = 9x + 6
3(2x + 4) =
9x + 6
6x + 12 = 9x + 6
9x + 6
12 = 3x + 6
2x + 4
6 = 3x
2 = x

30. HW Problems #18 Angle bisector 5.4 322-324 WS 3-7, 17-19, 34, 35
Constructing the Centroid and Orthocenter
#18
Angle bisector