Let AC and BD be two line segments that bisect each other at E, with AC & BD. Prove that ABCD...... K a. Prove that a quadrilateral whose diagonals are congruent and bisect each other is a rectangle. b. Explain how to use part (a) and only a compass and straightedge to construct any rectangle. c. Construct another rectangle not congruent to the rectangle in part (b) but whose diagonals are congruent to the diagona congruent? a. Let AC and BD be two line segments that bisect each other at E. with AC as BD Prove that ABCD is a rectangle. Because AC and BD bisect each other, Due to Because congruence. Because these angles are also Thus, m/ABC-mZDCB= (Simplify your answer.) Because b. Choose the correct answer below b. Choose the corect answer below it follows that they are therefore ABCD is a rectangle. a Prove that a quadrilateral whose diagonals are congruent and bisect each other is a rectangle b. Explain how to use part (a) and only a compass and straightedge to construct any rectangle e. Construct another rectangle not congruent to the rectangle in part (b) but whose diagonals are congruent to the diagonals of the rectangle in part (b). Why are the rectangles not congruent? OA. Construct two congruent line segments that perpendicularly bisect each other. The endpoints of these line segments will be the midpoints of the sides of a rectangle OB. Construct two congruent line segments that perpendicularly bisect each other. The endpoints of these line segments will be the vertices of a rectangle OC. Construct two congruent line segments that bisect each other. The endpoints of these line segments will be the midpoints of the sides of a rectangle OD. Construct two congruent line segments that bisect each other. The endpoints of these line segments will be the vertices of a rectangle c. Why are the rectangles not congruent? Choose the correct answer below CA. If the diagonals are not the same length the corresponding sides of the two rectangles will not be congruent OB the diagonals are not the same length and if the angles formed by the diagonals are not congruent the corresponding sides of the two rectangles will not be congruent OC. If the angles formed by the diagonals are not congruent the corresponding sides of the two rectangles will not be congruent 00. If the angles formed by the diagonals are not right angles, the corresponding sides of the two rectangles will not be congruent Next