1. Quiz Time

2. Special Segments in Triangles

3. Median
Median
Connect the vertex to
the opposite side's
midpoint

4. Altitude Altitude Connect the vertex to opposite side and is
perpendicular

5. The altitude is the “true height” of the triangle.
Tell whether each red segment is an altitude of the triangle.
The altitude is the “true height” of the triangle.
YES NO
YES

6. Angle Bisector Angle Bisector When the angle is cut into 2
congruent parts

7. Perpendicular Bisector
Go through a side's
midpoint and is
perpendicular

8. Tell whether each red segment is an perpendicular bisector of the triangle.NO NO
YES

9. Drill & Practice
Indicate which special triangle segment the red line is based on the picture and markings

10. Perpendicular Bisector
Who am I?
Perpendicular Bisector

11. Who am I?
Altitude

12. Who am I?
Angle Bisector

13. Who am I?
Median

14. Who am I?
Altitude

15. Who am I? 20
Angle Bisector

16. Start to memorize…
Indicate the special triangle segment based on its description

17. I cut an angle into two equal parts
Who am I?
I cut an angle into two equal parts
Angle Bisector

18. I connect the vertex to the opposite side’s midpoint
Who am I?
I connect the vertex to the opposite side’s midpoint
Median

19. I connect the vertex to the opposite side and I’m perpendicular
Who am I?
I connect the vertex to the opposite side and I’m perpendicular
Altitude

20. I go through a side’s midpoint and I am perpendicular
Who am I?
I go through a side’s midpoint and I am perpendicular
Perpendicular Bisector

21. Special Property of Medians

22. The intersection of the medians is called the CENTROID.
How many medians does a triangle have?

23. Vertex to CENTROID is TWICE as much as CENTROID to MIDPOINT
Theorem
Vertex to CENTROID is TWICE as much as CENTROID to MIDPOINT 2x x

24. C
How much is CX? D
CX = 2(XF) E X
CX = 2(13) 13 B A F
CX = 26

25. C
How much is XD? D
AX = 2(XD) E X 18
18 = 2(XD) B A F
9 = XD

26. In ABC, AN, BP, and CM are medians.
Ex: 1
In ABC, AN, BP, and CM are medians. C
If EM = 3, find EC. N
EC = 2(3) P E
EC = 6 B M A

27. In ABC, AN, BP, and CM are medians.
Ex: 2
In ABC, AN, BP, and CM are medians. C
If EN = 12, find AN. N
AE = 2(12)=24 P E B
AN = AE + EN M A
AN =
AN = 36

28. In ABC, AN, BP, and CM are medians.
Ex: 3
In ABC, AN, BP, and CM are medians.
If CM = 3x + 6, and CE = x + 12, what is x? A B M P E C N
CM = CE + EM
3x + 6 = (x + 12) + .5(x + 12)
3x + 6 = x x + 6
3x + 6 = 1.5x + 18
1.5x = 12
x = 8