question 2 of 10
how many lines of symmetry does a regular hexagon have?
a. none
b. 6
c. 3
d. 2

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Regular Hexagon Properties", "Polygon Symmetry" ], "new_concepts": [], "current_concepts": [ "Regular Hexagon Properties", "Polygon Symmetry" ] } ## Identify the properties of a regular hexagon A regular hexagon is a six-sided polygon with all sides of equal length and all interior angles of equal measure. ## Determine the lines of symmetry For any regular polygon with $n$ sides, the number of lines of symmetry is equal to $n$. - There are 3 lines of symmetry that pass through opposite vertices. - There are 3 lines of symmetry that pass through the midpoints of opposite sides. ## Calculate the total lines of symmetry $$ 3 \text{ (vertex-to-vertex)} + 3 \text{ (midpoint-to-midpoint)} = 6 $$

A. None

B. 6

C. 3

D. 2

{ "elements": [ { "type": "regularpolygon", "params": [[0, 0], [3, 0], 6], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.15)", "name": "Hexagon" } }, { "type": "line", "params": [[0, -4], [0, 4]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 1.5, "dash": 2, "name": "Symmetry Line 1" } }, { "type": "line", "params": [[-3.46, -2], [3.46, 2]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 1.5, "dash": 2 } }, { "type": "line", "params": [[-3.46, 2], [3.46, -2]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 1.5, "dash": 2 } }, { "type": "line", "params": [[-4, 0], [4, 0]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 1.5, "dash": 2, "name": "Symmetry Line 2" } }, { "type": "line", "params": [[-2, -3.46], [2, 3.46]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 1.5, "dash": 2 } }, { "type": "line", "params": [[-2, 3.46], [2, -3.46]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 1.5, "dash": 2 } } ], "timestamps": [0.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Polygon Symmetry" ] }

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Question

Explanation:

Identify the properties of a regular hexagon

Determine the lines of symmetry

Calculate the total lines of symmetry

Answer: