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Triangle Inequality

Sum of two si...

Question

Sum of two sides of a triangle is greater than the third side.

A

True

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B

False

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Solution

The correct option is A
True

The sum of two sides in a triangle will always be greater than the third side, otherwise, a triangle can not be formed.

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Question 71

State whether the statement is True or False.

Sum of two sides of a triangle is greater than or equal to the third side.

Q. 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.

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.

(c) Difference of any two sides of triangle is less than the third side.

Q. The sum of any two sides of a triangle is always

(a) equal to the third side
(b) less than the third side
(c) greater than or equal to the 3rd side
(d) greater than the 3rd side

State true or false for the following statement: Sum of any two sides of a triangle is greater than the third side.

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