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

$6=2KH$

$\frac{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

$18=3KI$

$\frac{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

$KG=2\times4$

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

Answer is

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

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

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

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