Question

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ments

ol geometry

which of the following rotational symmetries apply to the isosceles
triangle?

rotation

rotational symmetry of 120° about the origin

rotational symmetry of 180° about the origin

applies to the figure?

yes/no

yes/no

Explanation:

An isosceles triangle has only one line of symmetry (the line that bisects the vertex angle and is also the altitude and median). For rotational symmetry, a shape has rotational symmetry of order \(n\) if when rotated by \(\frac{360^{\circ}}{n}\) about a point (in this case, the origin), it maps onto itself.

• For a rotation of \(120^{\circ}\): An isosceles triangle (non - equilateral) does not map onto itself when rotated by \(120^{\circ}\) about the origin.
• For a rotation of \(180^{\circ}\): An isosceles triangle (non - equilateral) does not map onto itself when rotated by \(180^{\circ}\) about the origin.

Answer:

Rotational symmetry of \(120^{\circ}\) about the origin: No
Rotational symmetry of \(180^{\circ}\) about the origin: No