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

Explanation:

Step1: Recall properties of squares

All angles in a square are 90 degrees. So, if the side - lengths of two squares are equal, they are congruent.

Step2: Recall properties of rectangles

In rectangles, all angles are 90 degrees. For two rectangles to be congruent, the lengths of two adjacent (perpendicular) sides must be equal.

Answer:

a) C. The lengths of one side of each square must be equal
b) C. The lengths of the sides of two perpendicular sides of the rectangles must be equal