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 drawn 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.

Question

Philoid · Accepted Answer

(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.