Question

for each figure below, determine if it has rotational symmetry.
if it does, give the smallest angle of rotation needed for the figure to appear unmoved
rotational symmetry? yes no
angle?
rotational symmetry? yes no
angle?

Explanation:

Step1: Recall the definition of rotational symmetry

A figure has rotational symmetry if it can be rotated by an angle less than \(360^{\circ}\) and still look the same.

Step2: Analyze the equilateral triangle

An equilateral triangle has 3 equal sides and 3 equal angles. The formula for the angle of rotational symmetry is \(\frac{360^{\circ}}{n}\), where \(n\) is the number of times the figure coincides with itself in a \(360^{\circ}\) rotation. For an equilateral triangle, \(n = 3\). So, \(\frac{360^{\circ}}{3}=120^{\circ}\).

Step3: Analyze the letter \(T\)

If we rotate the letter \(T\) by any angle less than \(360^{\circ}\), it will not look the same.

Answer:

• For the equilateral triangle: Rotational symmetry? Yes, Angle: \(120^{\circ}\)
• For the letter \(T\): Rotational symmetry? No, Angle: N/A (since there is no rotational symmetry)