R. D. Sharma Solutions for Chapter: Congruent Triangles, Exercise 6: EXERCISE

The sum of any two sides of a triangle is _____ than the third side. [greater / smaller]

Fill in the blanks:

If two angles of a triangle are unequal, then the smaller angle has the _____ side opposite to it.

Difference of any two sides of a triangle is _____ than the third side. (Less/More/Equal)

If two sides of a triangle are unequal, then the larger side has _____ angle opposite to it. (Greater/Smaller)

$O$ is any point in the interior of $△ABC$. Prove that

$AB+AC>OB+OC$

$O$ is any point in the interior of $△ABC$. Prove that

$AB+BC+CA>OA+OB+OC$

$O$ is any point in the interior of $△ABC$. Prove that

$OA+OB+OC>\frac{1}{2}(AB+BC+CA)$

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