Centroid Theorem of a Triangle: states that the centroid of a triangle is at 2/3 of the distance from the vertex to the mid-point of the opposite side. Meaning:
[tex]QT=\frac{2}{3}VQ[/tex]
As the whole segment VQ is 3/3, then we can use this theorem:
[tex]VT=\frac{1}{3}VQ[/tex]
We could get a general rule which is:
[tex]\text{part of a segment=(either 1/3 \lbrack{}smaller part\rbrack{}or 2/3 \lbrack{}longer part\rbrack}\cdot wholesegment\text{)}[/tex]
Based on that, we know that 1/3 of the segment VQ equals VT, which equals 5 units. Then, to get VQ we would have to do the following:
[tex]VQ=VT\cdot3[/tex]
Then...
[tex]VQ=5\cdot3=15[/tex]
Now, to get QT:
[tex]QT=\frac{2}{3}VQ[/tex][tex]QT=\frac{2}{3}\cdot15=2\cdot5=10[/tex]
Answer:
• QT = 10
,
• QV = 15
