Question

what minimum information is sufficient to determine congruency for each of the following? a) two squares b) two rectangles c) two parallelograms a) what is the minimum information required to determine congruency for two squares? the lengths of two adjacent sides and an included angle of the two squares must be equal the lengths of one side and the measure of one angle of each square must be equal the lengths of one side of each square must be equal the measure of the angles of each square must be equal b) what is the minimum information required to determine congruency for two rectangles? a. the lengths of two perpendicular sides and the measure of one angle of each rectangle must be equal b. the lengths of two adjacent sides and an included angle of the two rectangles must be equal c. the lengths of the sides of two parallel sides of the rectangles must be equal d. the lengths of the sides of two perpendicular sides of the rectangles must be equal

Explanation:

Step1: Recall properties of squares

All angles in a square are 90 degrees and all sides are equal. So, if one - side length of two squares is equal, all other sides and angles will match due to these properties, and the squares are congruent.

Step2: Recall properties of rectangles

Rectangles have all angles equal to 90 degrees. For two rectangles to be congruent, the lengths of two perpendicular (adjacent) sides must be equal. Because once the lengths of two adjacent sides are equal, and all angles are 90 degrees, the rectangles will be congruent.

Step3: Recall properties of parallelograms

For two parallelograms to be congruent, the lengths of two adjacent sides and the included - angle must be equal. This is because these three pieces of information fix the shape and size of the parallelogram.

Answer:

a) The lengths of one side of each square must be equal
b) The lengths of two perpendicular sides of the rectangles must be equal
c) The lengths of two adjacent sides and an included angle of the two parallelograms must be equal