Question

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 diagonals of the rectangle in part (b). why are the rectangles not congruent?
b. choose the correct answer below
a. 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
b. construct two congruent line segments that perpendicularly bisect each other. the endpoints of these line segments will be the vertices of a rectangle
c. construct two congruent line segments that bisect each other. the endpoints of these line segments will be the vertices of a rectangle
d. 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
c. why are the rectangles not congruent? choose the correct answer below
a. if the angles formed by the diagonals are not right angles, the corresponding sides of the two rectangles will not be congruent
b. if the angles formed by the diagonals are not congruent, the corresponding sides of the two rectangles will not be congruent
c. if 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
d. if the diagonals are not the same length, the corresponding sides of the two rectangles will not be congruent

Explanation:

Step1: Recall rectangle properties

A rectangle has congruent and bisecting diagonals.

Step2: Analyze part b

To construct a rectangle using the property from part a, we construct two congruent line - segments that bisect each other. The endpoints of these segments are the vertices of the rectangle.

Step3: Analyze part c

Rectangles with congruent diagonals are not congruent if the angles formed by the diagonals are not congruent. This is because the side - lengths of the rectangles are determined by the lengths of the segments formed by the intersection of the diagonals, which depend on the angles between the diagonals.

Answer:

b. C. Construct two congruent line segments that bisect each other. The endpoints of these line segments will be the vertices of a rectangle.
c. B. If the angles formed by the diagonals are not congruent, the corresponding sides of the two rectangles will not be congruent.