Which of the following statements are true (T) and which are false (F)

1.	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.
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.

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.

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.