Question

Question is down below. Please help with each section, the drop down menus are the same for each one.

Answer 1

Recall that the centroid has the special property that, for each median, the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex.

1)

EH is median.

`FH=HG`
`\text{If FH=12 then HG=12.}`

2)

Here K is the centroid of the triangle and EH is the median.

We know that

`EK=2KH`

Substitute Ek=6 in the equation, we get

`6=2KH`

`(6)/(2)=KH`
`KH=3`
`\text{If }EK=6\text{ then KH=3}`

3)

Given that FI=18

We know that

`FI=2KI+KI`

`FI=3KI`

Substitute FI=18 in the equation, we get

`18=3KI`

`(18)/(3)=KI`
`KI=6`
`\text{If FI=18 then KI=}6`

4)

Given JK=4.

We know that

`KG=2JK`

Substitute JK=4 in the equation, we get

`KG=2*4`

`KG=8`
`\text{If JK=4 then KG=8}`

Answer is

`\text{If FH=12 then HG=12.}`

`\text{If }EK=6\text{ then KH=3}`

`\text{If FI=18 then KI=}6`

`\text{If JK=4 then KG=8}`