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Difference between Lengths of 2 Sides of a Triangle

Which of the ...

Question

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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Solution

The correct option is (d).
The difference between the length of any two sides of a triangle is always smaller than the length of the third side.
Hence, statement (d) is not correct.

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Similar questions

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. 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.

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

(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.

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.

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Difference between Lengths of 2 Sides of a Triangle

Standard VII Mathematics

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