In Fig. 10.131, prove that:

(i) CD + DA + AB + BC > 2AC

(ii) CD+DA +AB > BC

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

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

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.

Fill in the blanks to make the following statements true:

(i) In a right triangle the hypotenuse is the …….side.

(ii) The sum of three altitudes of a triangle is …… than its perimeter.

(iii) The sum of any two sides of a triangle is ….. than the third side.

(iv) If two angles of a triangle are unequal, then the smaller angle has the …. side opposite to it.

(v) Difference of any two sides of a triangle is ……. than the third side.

(vi) If two sides of a triangle are unequal, then the larger side has ……. angle opposite to it.