options: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
problem_activity: Task
Lisa makes an octagon by successively folding a square piece of paper as follows.  First, she folds the square in half vertically and horizontally and also along both diagonals leaving these creases:
[IMG]
Next, Lisa makes four more folds, identifying each pair of adjacent lines of symmetry for the square used for the folds in the first step:
[IMG]
Finally Lisa folds the four corners of her shape along the red creases marked below:
[IMG]
Explain why the shape Lisa has made is a regular octagon.


correct_option_index: 0