IM Geo.2.13 Lesson: Proofs about Parallelograms
Here is parallelogram ABCD and rectangle EFGH.
What do you notice? What do you wonder?
Conjecture: The diagonals of a parallelogram bisect each other.
Use the tools available to convince yourself the conjecture is true.
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?
Prove that segment bisects segment , and that segment bisects segment .
Here is a diagram:
Given: is a parallelogram with parallel to and parallel to . Diagonal is congruent to diagonal .
Prove: is a rectangle (angles , , , and 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 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.
Two intersecting segments always make a quadrilateral if you connect the endpoints.
What has to be true about the intersecting segments in order to make a rectangle?
What has to be true about the intersecting segments in order to make a rhombus?
What has to be true about the intersecting segments in order to make a square?
What has to be true about the intersecting segments in order to make a kite?
What has to be true about the intersecting segments in order to make an isosceles trapezoid?