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.

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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) The 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.

Justify the following statements with reasons:

(a) The sum of three sides of a triangle is more than the sum of its altitudes.

(b) The sum of any two sides of a triangle is greater than twice the median drawn to the third side.

Q. 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.

Fill in the blanks to make the statements true.

(a) In right triangle the hypotenuse is the __________ side.

(b) The sum of three altitudes of a triangle is __________ than its perimeter.

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

(e) Difference of any two sides of triangle is __________ than the third side.

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

Which of the following statements are not correct?

a) The sum of any two sides of a triangle is greater than the third side.
b) A triangle can have all its angles acute.
c) A right-angled triangle cannot be equilateral.
d) The difference of any two sides of a triangle is greater than the third side.

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