Does the equilateral triangle have rotational and line symmetry? Use words or diagrams to explain how you know.

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Welcome! Today we will explore the symmetry properties of an equilateral triangle. An equilateral triangle has both rotational and line symmetry. Let's examine these fascinating geometric properties step by step. Let's examine rotational symmetry first. An equilateral triangle has rotational symmetry of order 3. This means we can rotate it by 120 degrees around its center, and it will look exactly the same. We can do this rotation three times to complete a full 360-degree turn. Now let's explore line symmetry. An equilateral triangle has exactly three lines of symmetry. Each line passes through one vertex and the midpoint of the opposite side. If you fold the triangle along any of these lines, the two halves will match perfectly. Let's demonstrate both symmetries together. Watch as we rotate the triangle by 120 degrees three times - it returns to its original position, proving rotational symmetry. The dashed line shows one of the three lines of symmetry, demonstrating how the triangle can be perfectly folded along this line. To summarize what we have learned: An equilateral triangle possesses both rotational and line symmetry. It has rotational symmetry of order 3, meaning it looks identical after 120-degree rotations. It also has three lines of symmetry, each passing through a vertex and the midpoint of the opposite side. These symmetry properties make the equilateral triangle one of the most perfectly balanced shapes in geometry.