State which of the following statements are true and which are false :
Every equilateral triangle is an isosceles triangle .

Answer

To determine whether the statement "Every equilateral triangle is an isosceles triangle" is true or false, we can analyze the definitions of both types of triangles.

### Step 1: Understand the definition of an equilateral triangle.
An equilateral triangle is a triangle in which all three sides are equal in length. This means that if we have an equilateral triangle with sides of length 'a', then all sides are 'a'.

**Hint:** Remember that in an equilateral triangle, all sides are equal.

### Step 2: Understand the definition of an isosceles triangle.
An isosceles triangle is defined as a triangle that has at least two sides that are equal in length. This means that if we have an isosceles triangle, it can have two sides that are equal, while the third side can be different.

**Hint:** An isosceles triangle requires at least two sides to be equal.

### Step 3: Compare the definitions.
Since an equilateral triangle has all three sides equal, it naturally satisfies the condition of having at least two sides equal. Therefore, every equilateral triangle is also an isosceles triangle because it meets the criteria of having two equal sides.

**Hint:** Consider how the properties of equilateral triangles overlap with those of isosceles triangles.

### Step 4: Conclude the statement.
Based on the definitions and the comparison, we can conclude that the statement "Every equilateral triangle is an isosceles triangle" is true.

**Final Answer:** True.