which statements are true about the lines of symmetry of a regular pentagon? select three options. every line connects two vertices. every line connects the midpoints of 2 sides. every line bisects a vertex angle. every line bisects a side. every line is perpendicular to a side.
Which statements are true about the lines of symmetry of a regular pentagon? Select three options. Every line connects two vertices. Every line connects the midpoints of 2 sides. Every line bisects a vertex angle. Every line bisects a side. Every line is perpendicular to a side.
Answer:
To determine which statements are true about the lines of symmetry of a regular pentagon, we need to consider the properties of a regular pentagon and its lines of symmetry. A regular pentagon has five lines of symmetry, and each of these lines has specific characteristics. Let’s examine each statement:
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Every line connects two vertices.
- False: In a regular pentagon, the lines of symmetry do not connect two vertices. Instead, each line of symmetry passes through one vertex and the midpoint of the opposite side.
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Every line connects the midpoints of 2 sides.
- False: The lines of symmetry in a regular pentagon do not connect the midpoints of two sides. Each line of symmetry passes through a vertex and the midpoint of the opposite side.
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Every line bisects a vertex angle.
- True: Each line of symmetry in a regular pentagon bisects a vertex angle, dividing it into two equal parts.
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Every line bisects a side.
- True: Each line of symmetry bisects a side, dividing it into two equal segments.
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Every line is perpendicular to a side.
- True: Each line of symmetry is perpendicular to the side it bisects.
Therefore, the three true statements about the lines of symmetry of a regular pentagon are:
- Every line bisects a vertex angle.
- Every line bisects a side.
- Every line is perpendicular to a side.
These properties are consistent with the symmetrical nature of a regular pentagon and the way its lines of symmetry are defined.