1.7.3 Trying to Circle a Square
Instructions
1. Here is square ABCD with diagonal BD drawn:[br][br] a. Construct a circle centered at A with radius AD.[br][br] b. Construct a circle centered at C with radius CD.[br][br] c. Draw the diagonal AC.
Write a conjecture about the relationship between the diagonals BD and AC.
d. Label the intersection of the diagonals as point E. [br] (To do this, select the point and use the Style Bar to rename it. The Style Bar has the three lines with[br] the Circle and Triangle. Click on the AA button to name the point). [br][br] Then construct a circle with center at E and radius EB.
How are the diagonals related to the circle?
Use the knowledge you gained above and compass and straightedge moves to construct a square inscribed in a circle. Note: "inscribed" means the square will fit perfectly inside the circle.
Attribution
illustrative mathematics. geometry. unit 1. section 7. activity 3.[br]"Trying to Circle a Square"[br][url=https://im.kendallhunt.com/HS/teachers/2/1/7/index.html]https://im.kendallhunt.com/HS/teachers/2/1/7/index.html[br][/url]Licensed under the Creative Commons Attribution 4.0 license[br][url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url]
1.6.3 Parallel Construction Challenge
This is a tough one - challenge yourself![br][br]Here is a line, [i]m[/i], and a point, C, not on the line.[br][br]Use construction moves (straightedge and compass -- tools in the applet) [br]to construct a line PARALLEL to line [i]m[/i] that passes through point C.[br][br]Check that it passes the drag test. [br]Be prepared to share your reasoning.
Attribution
illustrative mathematics. geometry. unit 1. section 6. activity 3.[br]"Parallel Constructions Challenge"[br][url=https://im.kendallhunt.com/HS/teachers/2/1/6/index.html]https://im.kendallhunt.com/HS/teachers/2/1/6/index.html[br][/url]Licensed under the Creative Commons Attribution 4.0 license[br][url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url]