Use straightedge and compass tools to construct a square with segment [i]AB[/i] as one of the sides.

Here is square [i]ABCD[/i]  with diagonal [i]BD[/i] drawn:[list=1][*]Construct a circle centered at [i]A[/i] with radius [i]AD[/i] .[/*][*]Construct a circle [i]C [/i]centered at  with radius [i]CD[/i] .[/*][*]Draw the diagonal [i]AC[/i] and write a conjecture about the relationship between the diagonals [i]BD[/i] and [i]AC[/i] .[/*][*]Label the intersection of the diagonals as point [i]E[/i] and construct a circle centered at [i]E[/i] with radius [i]EB[/i]. [/*][/list]

Use your conjecture and straightedge and compass tools to construct a square inscribed in a circle.

IM G Unit 1 Lesson 7 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/1/7/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].