Question

In triangle DEF, DG = 10 cm. What is CG? 5 cm 10 cm 15 cm 20 cm

Answer 1

DG = 10 cm
CG = 1/2(DG) = 5 cm

answer
5cm

Answer 2

ANSWER

$CG=5cm$

EXPLANATION

In the given diagram, G is the point where all the three medians of the triangle meet.

We call this point of intersection of all the three medians the CENTROID of the triangle.

One property about the centroid is that, the centroid divides the medians in the ratio
$2:1$


The medians are the lines from the vertex to the midpoints of the opposite side of the triangle.

This implies that,

$DG:CG=2:1$

$10:CG=2:1$

We can rewrite this as,

$\frac{10}{ CG } = \frac{2}{1}$

We cross multiply to obtain,

$10 \times 1 = 2 \times CG$

$\Rightarrow CG = \frac{10}{2}$

$\Rightarrow CG = 5$

Therefore CG = 5cm