Geometry

Question Analysis:
This question is a comprehensive test of triangle classification based on both side lengths and angle measures.
The main focus is to assess the students' overall understanding of the relationships between different triangle types.

Key Concept Explanation:
An equilateral triangle has all sides equal and since it has at least two sides equal, it is also isosceles.
A right - angled triangle is defined by having one angle equal to 90°.
An acute - angled triangle (all angles less than 90°) can have all sides different (scalene) or at least two sides equal (isosceles).
An obtuse - angled triangle has one angle greater than 90°, and if it has two sides equal, it is an obtuse - angled isosceles triangle.

Step - by - Step Solution:
Analyze option A: By definition, an equilateral triangle meets the criteria for an isosceles triangle, so this statement is correct.
Analyze option B: The definition of a right - angled triangle is having one 90° angle, so this statement is correct.
Analyze option C: An acute - angled triangle's side lengths can vary, and it can be either scalene (all sides different) or isosceles (at least two sides equal), so this statement is correct.
Analyz...