Google Classroom
GeoGebraGeoGebra Classroom

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.
  1. Use the tools available to convince yourself the conjecture is true by constructing parallelogram ABCD.
  2. Convince your partner that the conjecture is true for any parallelogram. Can the 2 of you think of different ways to convince each other?
  3. What information is needed to prove that the diagonals of a parallelogram bisect each other?

  1. Prove that segment AC  bisects segment BD, and that segment BD bisects segment AC .

Image

Given: ABCD is a parallelogram with AB parallel to DC and AD parallel to BC. Diagonal AC is congruent to diagonal BD. Prove: ABCD is a rectangle (angles A, B, C, and D are right angles). With your partner, you will work backwards from the statement to the proof until you feel confident that you can prove that is a rectangle using only the given information. Start with this sentence: I would know ABCD is a rectangle if I knew _____________________. Then take turns saying this sentence: I would know [what my partner just said] if I knew __________________. . Write down what you each say. If you get to a statement and get stuck, go back to an earlier statement and try to take a different path.

IM G Unit 2 Lesson 13 from IM Geometry by Illustrative Mathematics, https://im.kendallhunt.com/HS/students/2/2/13/index.html. Licensed under the Creative Commons Attribution 4.0 license, https://creativecommons.org/licenses/by/4.0/.