The meeting point of the angle bisectors of a triangle is called the .

Consider the following statements:

$1.$The orthocentre of a triangle always lies inside the triangle.

$2.$The centroid of a triangle always lies inside the triangle.

$3.$The orthocentre of a right-angled triangle lies on the triangle.

$4.$The centroid of a right-angled triangle lies on the triangle.

Which of the above statements are correct?

Consider the following statements:

1. The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.

2. The point of intersection of the perpendiculars drawn from the vertices to the opposite sides of a triangle may lie on two sides.

Which of the above statements is/are correct?

How many medians are there in a triangle? 

In $\Delta DEF, DN, EO, FM$ are medians and point $P$ is the centroid. Find the following.

IF $PD=12$, then $PN=?$

In $\Delta DEF, DN, EO, FM$ are medians and point $P$ is the centroid. Find the following.

IF $DE=44$, then $DM=?$

In the figure, identify the Median.

In $\Delta DEF, DN, EO, FM$ are medians and point $P$ is the centroid.

If $DO=8$, then $FD=?$

Draw all three altitudes for the following triangles and explain how they are different:

If $CG$ is the median of $\mathrm{\Delta }\mathrm{E}\mathrm{C}\mathrm{D},\mathrm{}$ what is the mid-point of side $ED$?

If $\mathrm{\Delta }\mathrm{E}\mathrm{B}\mathrm{D}$ is a right triangle, name the two altitudes of $△\mathrm{EBD}$.

In the given figure, if $C$ is the midpoint of $BD$, name the median of $△EBD$.

If $CF\perp ED$, name the altitude of $\mathrm{\Delta }\mathrm{E}\mathrm{C}\mathrm{D}.$

Write the definition of the median of a triangle.