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IM Geometry Unit 2 Lesson 12

Playing with Parallelograms

  1. Which figures (if any) are always rectangles? Which figures can be dragged to make a rectangle?

  1. Which figures (if any) are always parallelograms? Which figures can be dragged to make a parallelogram?

Here are some conjectures:
  • All rectangles are parallelograms.
  • If a parallelogram has (at least) one right angle, then it is a rectangle.
  • If a quadrilateral has 2 pairs of opposite sides that are congruent, then it is a parallelogram.
  • If the diagonals of a quadrilateral both bisect each other, then the quadrilateral is a parallelogram.
  • If the diagonals of a quadrilateral both bisect each other and they are perpendicular, then the quadrilateral is a rhombus.
  1. Pick one conjecture and use technology to convince yourself it is true.
  2. Rewrite the conjecture to identify the given information and the statement to prove.
  3. Draw a diagram of the situation. Mark the given information and any information you can figure out for sure.

  1. Write a rough draft of how you might prove your conjecture is true.

IM G Unit 2 Lesson 12 from IM Geometry by Illustrative Mathematics, https://im.kendallhunt.com/HS/students/2/2/12/index.html. Licensed under the Creative Commons Attribution 4.0 license, https://creativecommons.org/licenses/by/4.0/.