QQuestionMathematics
QuestionMathematics
Consider the reflectional symmetry of the regular pentagon.
How many lines of symmetry does the pentagon have?
A. 1
B. 3
C. 5
D. 6
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understand Reflectional Symmetry
Reflectional symmetry occurs when an object can be divided into identical halves by drawing a line through its center. When the object is folded along this line, the two halves perfectly overlap.
Step 3:: Analyze the Regular Pentagon
A regular pentagon has 5 equal sides and 5 equal angles. To find lines of symmetry, we need to consider how many ways we can divide the pentagon into identical halves through its center.
Step 4:: Identify Symmetry Lines
In a regular pentagon, we can draw lines of symmetry: - From each vertex to the opposite vertex - Passing through the center of the pentagon - Dividing the pentagon into two equal parts
Step 5:: Count the Symmetry Lines
By carefully drawing these lines, we can see that there are 5 distinct lines of symmetry: - One line through each vertex to the opposite vertex - These lines pass through the center of the pentagon - Each line divides the pentagon into two identical halves
Step 6:: Verify the Number of Symmetry Lines
5 \text{ symmetry lines} = \text{Number of vertices in the pentagon}
Final Answer
The regular pentagon has 5 lines of symmetry, corresponding to the 5 vertices of the pentagon.
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