1. Medians

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

3. Who am I?
Median

4. Perpendicular Bisector
Who am I?
Perpendicular Bisector

5. Who am I?
Altitude

6. Who am I?
Angle Bisector

7. Who am I?
Altitude

8. Who am I? 20
Angle Bisector

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

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

11. Special Property of Medians

12. How many medians does a triangle have?
CENTROID:The intersection of all 3 Medians.
The Centroid is also the Center of Gravity

13. 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

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

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

16. 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

17. 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

18. EB =22 2(3x+2)=8x-2 If PE = 3x+2, find EB=7x-1 C Find EB. N
If PE = 3x+2, find EB=7x-1
Find EB. C N
2 times small = big P E
2(3x+2)=8x-2 B M A
EB =22