Question

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 1

True are:
- Every line bisects a vertex angle.
- Every line bisects a side.
- Every line is perpendicular to a side.

Reason: In a regular pentagon each symmetry axis runs through a vertex and the midpoint of the opposite side. So it bisects that vertex angle, meets and bisects the opposite side at its midpoint, and — since a radius to a side's midpoint is perpendicular to that side — the axis is perpendicular to that side. The statements about connecting two vertices or connecting two midpoints are false.