Question

In triangle QUW, Point T is the centroid,and VT=5 . find QT and VQ .

Answer 1

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:

`QT=(2)/(3)VQ`

As the whole segment VQ is 3/3, then we can use this theorem:

`VT=(1)/(3)VQ`

We could get a general rule which is:

`\text{part of a segment=(either 1/3 \lbrack{}smaller part\rbrack{}or 2/3 \lbrack{}longer part\rbrack}\cdot wholesegment\text{)}`

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:

`VQ=VT\cdot3`

Then...

`VQ=5\cdot3=15`

Now, to get QT:

`QT=(2)/(3)VQ`
`QT=(2)/(3)\cdot15=2\cdot5=10`

Answer:

• QT = 10

,

• QV = 15