1. A segment that connects a vertex of a triangle
to the midpoint of the opposite side.
The point of concurrency of the medians
of a triangle.
The perpendicular segment from a vertex of a
triangle to the opposite side.
The point of concurrency of the altitudes of a
triangle.

2. AE BF CD
Also, EP = 1/3AE, FP = 1/3BF, and DP = 1/3CD
Therefore, AP = 2EP, BP = 2FP, and CP = 2DP

3. GM
2/3 /3 6 9
3/2 GM

4. FM = 2/3FK
10 = 2/3FK
15 = FK
MK = 1/2FM
MK = 1/2(10)
MK = 5

5.
(4, 3)
two thirds 2/ 2
4, 4
If you don't have a horizontal or vertical line as a median
you would have to use the distance formula to find the length
of the median, then take 2/3 of the length to find the centroid.

6. concurrent

7. Orthocenter
Orthocenter

8. Point K should be moved to (4, 9)

9. ∠ADB
∠CDB
Altitude
HL Congruence Theorem CD
Midpoint

10. AB ≅ CB
Given
∠ADB ≅ ∠CDB
All right ∠'s are ≅
BD ≅ BD
Reflexive Property
∆ABD ≅ ∆CBD
HL ≅ Thm
∠ABD ≅ ∠CBD
CPCTC
BD is an ∠ bisector
Definition of bisector
Statements Reasons