Question

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

Explanation:

Step1: Recall properties of squares

All angles in a square are 90° and all - sides are equal. So, if the side - length of two squares is equal, they are congruent.

Step2: Recall properties of rectangles

Rectangles have all angles equal to 90°. If the lengths of two perpendicular sides (length and width) of two rectangles are equal, the rectangles are congruent.

Step3: Recall properties of parallelograms

By the Side - Angle - Side (SAS) congruence criterion for parallelograms, if the lengths of two adjacent sides and the included angle of two parallelograms are equal, the parallelograms are congruent.

Answer:

a) The side - length of the two squares must be equal.
b) C. The lengths of the sides of two perpendicular sides of the rectangles must be equal.
c) A. The lengths of two adjacent sides and an included angle of the two parallelograms must be equal.