Which of the following statements is not true?

Q: Which of the following statements is not true?

Which of the following statements is not true?

Question

Accepted Answer

The correct option is 3:
The correct option is 3 because the statement, "Triangle, which has all three angles obtuse, is called obtuse-angled triangle," fundamentally contradicts the geometric properties of a triangle. A cardinal rule of Euclidean geometry states that the sum of the interior angles of any triangle must be exactly 180 degrees. An obtuse angle, by definition, is an angle greater than 90 degrees and less than 180 degrees. If a triangle were to have even two obtuse angles, their sum would already exceed 180 degrees (e.g., 91° + 91° = 182°), making the formation of a closed three-sided figure impossible. Therefore, an obtuse-angled triangle can only ever have *one* obtuse angle, with the other two angles necessarily being acute. This makes the statement factually incorrect, and thus the one that is "not true."

The incorrect option is 1:
The statement "A triangle, having one angle right angle, is called right-angled triangle" is absolutely true and is the precise definition of this type of triangle. A right angle is an angle that measures exactly 90 degrees. By definition, a triangle can be classified as a right-angled triangle if it contains a single 90-degree angle. This characteristic means that the remaining two angles must both be acute and their sum must equal 90 degrees to satisfy the total sum of 180 degrees. This classification is a cornerstone of geometry, especially serving as the basis for the application of the Pythagorean theorem.

The incorrect option is 2:
The statement "An equilateral triangle is always an Acute-angled triangle" is a true statement derived from the core properties of these shapes. An equilateral triangle is defined as having all three sides of equal length, which necessarily means all three interior angles are also equal. To total 180 degrees, each angle must measure exactly 60 degrees (180 / 3 = 60). Since an acute angle is defined as any angle measuring less than 90 degrees, and 60 degrees is less than 90 degrees, all angles in an equilateral triangle are acute. This confirms that all equilateral triangles fit the precise definition of being acute-angled triangles.

The incorrect option is 4:
The statement "Acute-angled triangle has all three angles acute" is the definitive and true statement used to classify a triangle by its angles. A triangle is designated as an acute-angled triangle if and only if every single one of its three interior angles measures less than 90 degrees. Even though all three angles are acute, their total sum must still strictly equal 180 degrees. This category distinguishes itself from both the right-angled triangle (which has one 90° angle) and the obtuse-angled triangle (which has one angle greater than 90°).