Which of the following statements are true (T) and which are false (F)?
(i) Sum of the three sides of a triangle is less than the sum of its three altitudes.
(ii) Sum of any two sides of a triangle is greater than twice the median drown to the third side
(iii) Sum of any two sides of a triangle is greater than the third side.
(iv) Difference of any two sides of a triangle is equal to the third side.
(v) If two angles of a triangle are unequal, then the greater angle has the larger side opposite to it
(vi) 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.
(i) False (F)
Reason: Sum of these sides of a triangle is greater than sum of its three altitudes
(ii) True (T)
(iii) True (T)
(iv) False (F)
Reason: The difference of any two sides of a triangle is less than third side
(v) True (T)
Reason: The side opposite to greater angle is longer and smaller angle is shorter in a triangle
(vi) True (T).
Reason: The perpendicular distance is the shortest distance from a point to a line not containing it.