Medians of a Triangle

Define centroid of a triangle. Write its properties and the formula for centroid of a triangle.

Define median of a triangle and write its properties.

Write the difference between the median and the altitude of a triangle.

The incenter of a triangle is the point of intersection of all the perpendicular bisectors of the sides of a triangle. 

The incentre always lies inside the triangle.

Prove that the incentre of a triangle is equidistant from its sides.

If $G$ is the centroid of a $△ABC$ and $P$ is any other point in the plane, then $P{A}^2+P{B}^2+P{C}^2$ is equal to

The $3$ medians divide the triangle into $8$ smaller triangles of equal area.

Every triangle has$3$ medians.

 Given $AM$ is the median, which of the following statements is false?

$ABC$ is an isosceles triangle with $AB=AC$. $BD$ and $CE$ are two medians of the triangle. Then $BD=$........

Point G is the centroid of $∆ ABC$.

 If $l\left(AP\right) =6$ then $l\left(GP\right) =$?

Point $G$ is the centroid of $∆ ABC$. If $l\left(BG\right) = 6$, then find $l\left(BQ\right)$.

Point G is the centroid of $∆ ABC$.

If $l\left(RG\right) = 2.5$ then $l\left(GC\right) =$?

$AD$ is a median of the triangle $ABC$. If $AB+BC+CA>x$ then find $x$.

 $G$ is the centroid of triangle $ABC$ and $BF=10$. If the length of $FA$ is $x$ then find $x$.

 The centroid is the point of concurrency of the _____of a triangle.

 Which of the following describes a median of a triangle?

In $△ABC,$ the median $AD, BE$ and $CF$ passes through the point $G$. If $AD=7.5 \mathrm{cm},$ then find $GD$ (in $\mathrm{cm}$) (correct up to one decimal place)

In $△ABC,$ the median $AD, BE$ and $CF$ passes through the point $G$. If $GF=4 \mathrm{cm}$ then, find $GC$ (in $\mathrm{cm}$).