A triangle, in which all angles are the same, is known as :

Question

Accepted Answer

A triangle in which all angles are the same is known as an equilateral triangle. This is because, by definition, an equilateral triangle has three equal sides and three equal angles. Each angle in an equilateral triangle measures 60 degrees, making the sum of the angles 180 degrees, which is consistent with the properties of a triangle.

1. **Explanation for Option 1 (Equilateral triangle):**
   - An equilateral triangle is characterized by having all three sides of equal length. Consequently, this equality in side lengths results in all three internal angles being equal as well. Since the sum of the angles in any triangle is always 180 degrees, each angle in an equilateral triangle measures 60 degrees. This uniformity in angle measurement is the defining feature of an equilateral triangle, making Option 1 the correct answer.

2. **Explanation for why other options are incorrect:**
   - **Option 2 (Isosceles triangle):** An isosceles triangle has at least two sides of equal length, which means it has at least two equal angles. However, the third angle can be different, so not all angles are necessarily the same. Therefore, an isosceles triangle does not fit the criteria of having all angles equal.
   - **Option 3 (Scalene triangle):** A scalene triangle has all sides of different lengths, which means all angles are also different. This directly contradicts the condition of having all angles the same, making this option incorrect.
   - **Option 4 (Right-angled triangle):** A right-angled triangle has one angle that is exactly 90 degrees. The other two angles must add up to 90 degrees, but they are not necessarily equal to each other. Therefore, a right-angled triangle cannot have all angles the same, making this option incorrect.

In conclusion, the only type of triangle where all angles are equal is an equilateral triangle, which is why Option 1 is the correct answer.