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Which of the following statements is 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. Difference of any two sides of a triangle is greater than the third side

Solution:

We have to find the statement which is not correct.

(i) The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

considering 3 cm, 4 cm, 5 cm

Let the two sides be 3cm and 4cm

Let the third side be 5 cm

Now, sum of two sides = 3 + 4 = 7 cm

So, 7 > 5

(ii) A triangle can have all its angles acute

An acute angle is a type of angle that measures less than 90° i.e. measure between 0° to 90°.

Consider a triangle ABC,

Let ∠A = 60°, ∠B = 40° and ∠C = 80°

All the angles are acute since it's less than 90 degrees.

We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 60° + 40° + 80°

= 100° + 80°

= 180°

Therefore, all the angles of a triangle can be acute.

(iii) A right-angled triangle cannot be equilateral

In a right angle triangle, one angle is 90°

Consider a triangle ABC,

By angle sum property of a triangle,

∠A + ∠B + ∠C = 180°

∠A + 90° + ∠C = 180°

∠A + ∠C = 180° - 90°

∠A + ∠C = 90°

An equilateral triangle is a triangle that has all its sides equal in length.

The three angles of the equilateral triangle are congruent and equal to 60 degrees.

Therefore, a right angled triangle cannot be equilateral.

✦ Try This: In △ABC, if ∠B = 90° and ∠C = 45°, find ∠A (in degrees)

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 18

Which of the following statements is 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. Difference of any two sides of a triangle is greater than the third side

Summary:

Out of the following, the difference of any two sides of a triangle is greater than the third side is not correct

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