Question

select all the true statements.
a two rhombuses with the same side lengths are always congruent.
b two squares with the same side lengths are always congruent.
c two quadrilaterals with the same side lengths are always congruent.
d two rectangles with the same side lengths are always congruent.
e two parallelograms with the same side lengths are always congruent.

Explanation:

• For option A:
• A rhombus has all sides equal. But two rhombuses with the same side - lengths may have different angles. So, they are not always congruent.
• For option B:
• 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 (SSS) congruence criterion (since all four sides are equal and all four angles are equal), they are congruent.
• For option C:
• A quadrilateral is a general four - sided figure. Two quadrilaterals with the same side - lengths can have different angles (e.g., a square and a rhombus with the same side - lengths are not congruent as their angles are different in general).
• For option D:
• A rectangle has opposite sides equal. If two rectangles have the same side - lengths (i.e., length and width are equal), by the Side - Side - Side - Side (SSSS) congruence (since opposite sides are equal and all angles are \(90^{\circ}\)), they are congruent.
• For option E:
• A parallelogram has opposite sides equal. But two parallelograms with the same side - lengths can have different angles. So, they are not always congruent.

Answer:

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