TWO THIRD CENTRIOD THEOREM OF A TRIANGLE

The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.

Problem 1 :

Given that AG = 14 , FG = 10 and EB = 36, find

i) GD ii) AD iii) CG iv) CF v) EG and vi) BG

Solution :

Finding GD and AD :

Finding CG and CF :

Finding EG and BG :

i) GD = 7

ii) AD = 21

iii) CG = 20

iv) CF = 30

v) EG = 12

vi) BG = 24

Problem 2 :

Given that AD = 15, GE = 19 and FG = 6, find

i) AG ii) GD iii) BG iv) BE v) CF and vi) CG

Solution :

Finding AG and GD :

Finding BD and BE :

Finding CG and CF :

i) AG = 10

ii) GD = 5

iii) BG = 38

iv) BE = 57

v) CF = 18

vi) CG = 12

Problem 3 :

Given that CF = 9, GD = 2 and BG = 16, find

i) CG ii) GF iii) AG iv) AD v) GE and vi) BE

Solution :

Finding CG and GF :

Finding AG and AD :

Finding GE and BE :

i) CG = 6

ii) GF = 3

iii) AG = 4

iv) AD = 6

v) GE = 8

vi) BE = 24

Problem 4 :

Given that BE = 27, DG = 4 and CG = 10, find

i) BG ii) GE iii) GA iv) DA v) CF and vi) GF

Solution :

Finding BG and GE :

Finding GA and AD :

Finding CF and GF :

i) BG = 18

ii) GE = 9

iii) GA = 8

iv) DA = 12

v) CF = 15

vi) GF = 5

TWO THIRD CENTRIOD THEOREM OF A TRIANGLE

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