3. Will an altitude always lie in the interior of a triangle? If you think that this need not betrue, draw a rough sketch to show such a case

No, an altitude of a triangle will not always lie in the interior of the triangle. This is especially true for obtuse triangles.

In an obtuse triangle, one angle is greater than 90 degrees. When you draw an altitude from the vertex of the obtuse angle, it will fall outside the triangle.

Here's a rough sketch to illustrate this:

     A
    / \
   /   \
  /     \
 /       \
B---------C
 \       /
  \     /
   \   /
    \ /
     D

In the above obtuse triangle ABC, AD is the altitude from the vertex A. As you can see, the altitude AD lies outside the triangle.