Question

If M is the centroid of triangle GHI, HL=45, JI=63, and KG=60, find the missing measures

Answer 1

Part a)
`ML=15\ units`

Part b)
`HM=30\ units`

Part c)
`JM=21\ units`

Part d)
`MI=42\ units`

Part e)
`GM=40\ units`

Part f)
`MK=20\ units`

Explanation:

see the attached figure to better understand the problem

we know that

A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle.

The centroid is located two thirds of the distance from any vertex of the triangle

Part a) Find ML

we have

`HL=45\ units`

we know that

`ML=(1)/(3)HL`

substitute the given value

`ML=(1)/(3)(45)`

`ML=15\ units`

Part b) Find HM

we have

`HL=45\ units`

we know that

`HM=(2)/(3)HL`

substitute the given value

`HM=(2)/(3)(45)`

`HM=30\ units`

Part c) Find JM

we have

`JI=63\ units`

we know that

`JM=(1)/(3)JI`

substitute the given value

`JM=(1)/(3)(63)`

`JM=21\ units`

Part d) Find MI

we have

`JI=63\ units`

we know that

`MI=(2)/(3)JI`

substitute the given value

`MI=(2)/(3)(63)`

`MI=42\ units`

Part e) Find GM

we have

`KG=60\ units`

we know that

`GM=(2)/(3)KG`

substitute the given value

`GM=(2)/(3)(60)`

`GM=40\ units`

Part f) Find MK

we have

`KG=60\ units`

we know that

`MK=(1)/(3)KG`

substitute the given value

`MK=(1)/(3)(60)`

`MK=20\ units`