What do you notice? What do you wonder? 

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.

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?