Which figures (if any) are always rectangles? Which figures can be dragged to make a rectangle?[br]

Which figures (if any) are always parallelograms? Which figures can be dragged to make a parallelogram?[br]

[list][/list]Here are some conjectures:[br][list][*]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.[/*][/list]Pick one conjecture and use technology to convince yourself it is true.[br]

Rewrite the conjecture to identify the given information and the statement to prove.[br]

Write a rough draft of how you might prove your conjecture is true.[br]

Exchange proofs with your partner. Read the rough draft of their proof. If it convinces you, write a detailed proof together following their plan. If it does not convince you, suggest changes that will make the proof convincing.

Draw 2 circles (of different sizes) that intersect in 2 places. Label the centers [math]A[/math] and [math]B[/math] and the points of intersection [math]C[/math] and [math]D[/math]. Prove that segment [math]AB[/math] must be perpendicular to segment [math]CD[/math].