Becky is writing a coordinate proof to show that the diagonals of a parallelogram bisect each other. She starts by assigning coordinates as given. A parallelogram graphed on a coordinate plane. The parallelogram is labeled A B C D. The coordinates of vertex A are 0 comma 0. The coordinates of vertex B a comma 0. The coordinates of vertex C are not labeled. The coordinates of vertex D are b comma c. Diagonals A C and B D intersect at point E whose coordinates are not labeled.

Drag and drop the correct answer into each box to complete the proof.

The coordinates of point C are (Response area, c).

The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (a+b2, c2) .

The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are (Response area, c2).

AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates (a+b2,Response area)..

By the definition of midpoint, AE¯¯¯¯¯≅Response area and Response area≅DE¯¯¯¯¯.

Therefore, diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.

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