Which of the following statements are true (T) and which are false (F)? Sum of the three sides of a triangle is less than the sum of its three altitudes. Sum of any two sides of a triangle is greater than twice the median drawn to the third side. Sum of any two sides of a triangle is greater than the third side. Difference of any two sides of a triangle is equal to the third side. If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it. Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.

Explanation

Solution
'(i)' False:
Sum of three sides of a triangle is greater than sum of its three altitudes.
'(ii)' True
'(iii)' True
'(iv)' False:
The difference of any two sides of a triangle is less than the third side.
'(v)' True:
The side opposite to greater angle is longer and smaller angle is shorter in a triangle.
'(vi)' True:
The perpendicular distance is the shortest distance from a point to a line not containing it.