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?

The locus of a point equidistant from two intersecting lines is:

Consider the following statements :

Two triangles are said to be congruent, if

$1.$ Three angles of one triangle are equal to the corresponding three angles of the other triangle.

$2.$ Three sides of one triangle are equal to the corresponding three sides of the other triangle.

$3.$ Two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle.

$4.$ Two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.

Which of the above statements are correct?

Given that the angles of a polygon are all equal and each angle is a right angle.

Statement-$1$: The polygon has exactly four sides.

Statement-$2$: The sum of the angles of a polygon having $n$ sides is $(3n-8)$ right angles.

Which one of the following is correct in respect of the above statements?