Question

1. select all the true statements.

a. two squares with the same side lengths are always congruent.
b. two rectangles with the same side lengths are always congruent.
c. two rhombuses with the same side lengths are always congruent.
d. two parallelograms with the same side lengths are always congruent.

Explanation:

• For A:
• A square has all sides equal and all angles equal to \(90^{\circ}\). If two squares have the same side lengths, by the Side - Side - Side - Side (SSSS) congruence criterion (for quadrilaterals, when all four sides and all four angles are equal), they are congruent.
• For B:
• A rectangle has opposite sides equal and all angles equal to \(90^{\circ}\). If two rectangles have the same side lengths (i.e., length \(l_1 = l_2\) and width \(w_1=w_2\)), by the Side - Angle - Side - Angle (SASA) congruence criterion (for rectangles, adjacent sides and included angles (which are \(90^{\circ}\))), they are congruent.
• For C:
• A rhombus has all sides equal, but the angles can vary. Two rhombuses with the same side lengths may have different angle measures. For example, one rhombus with angles \(60^{\circ}\) and \(120^{\circ}\) and another with angles \(80^{\circ}\) and \(100^{\circ}\) (while having the same side lengths) are not congruent.
• For D:
• A parallelogram has opposite sides equal. But the angles can vary. Two parallelograms with the same side lengths may have different angle measures. For example, one parallelogram with angles \(30^{\circ}\) and \(150^{\circ}\) and another with angles \(40^{\circ}\) and \(140^{\circ}\) (while having the same side lengths) are not congruent.

Answer:

A. Two squares with the same side lengths are always congruent; B. Two rectangles with the same side lengths are always congruent.