IM Geometry Unit 2 Lesson 13
Notice and Wonder: Diagonals
What do you notice? What do you wonder?
Conjecture: The diagonals of a parallelogram bisect each other.[br][list=1][*]Use the tools available to convince yourself the conjecture is true by constructing parallelogram [i]ABCD.[/i][/*][*]Convince your partner that the conjecture is true for any parallelogram. Can the 2 of you think of different ways to convince each other?[/*][*]What information is needed to prove that the diagonals of a parallelogram bisect each other?[/*][/list]
[list=1][*]Prove that segment [i]AC[/i] bisects segment [i]BD[/i], and that segment [i]BD[/i] bisects segment [i]AC[/i] .[/*][/list]
Given: [i]ABCD[/i] is a parallelogram with [i]AB [/i]parallel to [i]DC[/i] and [i]AD[/i] parallel to [i]BC[/i].[br]Diagonal [i]AC [/i]is congruent to diagonal [i]BD[/i].[br]Prove: [i]ABCD[/i] is a rectangle (angles [i]A, B, C, [/i]and [i]D [/i]are right angles).[br][br]With your partner, you will work backwards from the statement to the proof until you feel[br]confident that you can prove that is a rectangle using only the given information.[br][br]Start with this sentence: I would know [i]ABCD[/i] is a rectangle if I knew _____________________.[br]Then take turns saying this sentence: I would know [what my partner just said] if I knew __________________.[br].[br]Write down what you each say. If you get to a statement and get stuck, go back to an[br]earlier statement and try to take a different path.
IM G Unit 2 Lesson 13 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/2/13/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].