the figure below is an isosceles triangle.
which of the following rotational symmetries apply to the isosceles triangle?

rotation | applies to the figure?
rotational symmetry of $120^\circ$ about the origin | yes/no
rotational symmetry of $180^\circ$ about the origin | yes/no

Question

the figure below is an isosceles triangle.
which of the following rotational symmetries apply to the isosceles triangle?

rotation | applies to the figure?
rotational symmetry of $120^\circ$ about the origin | yes/no
rotational symmetry of $180^\circ$ about the origin | yes/no

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rotational Symmetry" ], "new_concepts": [], "current_concepts": [ "Rotational Symmetry", "Geometric Transformations" ] } ## Identify the vertices of the isosceles triangle $$ \begin{aligned} &V_1 = (-4, 8)\ &V_2 = (-4, -4)\ &V_3 = (8, -4) \end{aligned} $$ ## Determine the rotational symmetry of the figure $$ \begin{aligned} &\text{An isosceles triangle that is not equilateral has only } 360^\circ \text{ rotational symmetry (order 1).}\ &\text{Rotation of } 120^\circ \text{ about the origin does not map the triangle onto itself.}\ &\text{Rotation of } 180^\circ \text{ about the origin does not map the triangle onto itself.} \end{aligned} $$ | Rotation | Applies to the figure? | |---|---| | Rotational symmetry of $120^\circ$ about the origin | No | | Rotational symmetry of $180^\circ$ about the origin | No | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Rotational Symmetry" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vertices of the isosceles triangle

Determine the rotational symmetry of the figure

Answer: