Manipur Board Solutions for Chapter: Triangles, Exercise 3: EXERCISE 7.3

If $D$ is any point on the base $BC$ produced of an isosceles triangle $ABC$, prove that $AD>AB$.

Of all the line segments that can be drawn to a given line, from a point, not lying on it, prove that the perpendicular line segment is the shortest.

Prove that the perimeter of a triangle is greater than the sum of its three medians.

Show that the difference of any two sides of a triangle is less than the third side.

Prove that in quadrilateral, the sum of all the sides is greater than the sum of its diagonals.

In $∆PQR, S$ is any point on the side $QR$. Show that $PQ+QR+PR>2PS$.