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.[br]
Convince your partner that the conjecture is true for any parallelogram. Can the 2 of you think of different ways to convince each other?[br]
What information is needed to prove that the diagonals of a parallelogram bisect each other?[br]
Prove that segment [math]AC[/math] bisects segment [math]BD[/math], and that segment [math]BD[/math] bisects segment [math]AC[/math].[br]
Here is a diagram:[br][img]data:image/png;base64,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[/img][br]Given: [math]ABCD[/math] is a parallelogram with [math]AB[/math] parallel to [math]CD[/math] and [math]AD[/math] parallel to [math]BC[/math]. Diagonal [math]AC[/math] is congruent to diagonal [math]BD[/math].[br]Prove: [math]ABCD[/math] is a rectangle (angles [math]A[/math], [math]B[/math], [math]C[/math], and [math]D[/math] are right angles).[br]With your partner, you will work backwards from the statement to the proof until you feel confident that you can prove that [math]ABCD[/math] is a rectangle using only the given information.[br]Start with this sentence: I would know [math]ABCD[/math] 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]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?[br]
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?

IM Geo.2.13 Practice: Proofs about Parallelograms

Conjecture:
[size=150]A quadrilateral with one pair of sides both congruent and parallel is a parallelogram.[/size][br][br][list][*]Draw a diagram of the situation. [/*][*]Mark the given information. [/*][/list]
Restate the conjecture as a specific statement using the diagram.[br]
Here is a quadrilateral ABCD.
[size=150][math]AD[/math] is congruent to [math]BC[/math], and [math]AD[/math] is parallel to [math]BC[/math].[/size][br][br]Show that [math]ABCD[/math] is a parallelogram.
ABDE is an isosceles trapezoid.
Name one pair of congruent triangles that could be used to show that the diagonals of an isosceles trapezoid are congruent.
Select the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other.
[img]data:image/png;base64,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[/img]
Here is a diagram:
[img]https://i.ibb.co/943hTgZ/Geo-2-13-5.png[/img][br][br]Is triangle [math]EJH[/math] congruent to triangle [math]EIH[/math]?[br]Explain your reasoning.
Select [b]all [/b]true statements based on the diagram.[br][br][img]data:image/png;base64,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[/img]
Which conjecture is possible to prove?

Information