Question

Why can't a parallelogram and a rhombus, as shown in the figure never be congruent?

• A. They have unequal side lengths.
• B. They have unequal vertex angles.
• C. No, they are congruent.

Answer 1

The correct option is A They have unequal side lengths.

Concept: For two figures to be congruent, they must have equal shape as well as size.

In a parallelogram, the opposite sides are equal.
In the given figure, two sides of the parallelogram measures $8\text{cm},$ but the other two are of $6\text{cm}$ in length.

However, for a rhombus, all the four sides are equal in length, in this case $6\text{cm}$.

Also, the corresponding angles can be same as it is not mentioned.

$\therefore$ They cannot be congruent.