Question

For the following figure, can you deduce from the information “$\overline{AB},\overline{BC},\overline{CD}$ and$\overline{DA}$ are all congruent” that quadrilateral ABCD is a parallelogram. If so, what theorem can you use?

Short answer

The quadrilateral ABCD is a parallelogram.

Step-by-step solution

Step 1- Check the figure.

Consider the figure.

Step 2- Apply the concept of parallelogram.

A square is quadrilateral with all sides congruent and rhombus also a quadrilateral with all four sides congruent.

Step 3- Step description.

Consider $\overline{AD},\overline{BC},\overline{CD},\overline{DA}$ are all congruent.

Consider the fact that as a square is quadrilateral with all sides congruent and rhombus also a quadrilateral with all four sides congruent.

ThusABCD is either square or rhombus.

But every square as well as every rhombus is a parallelogram, thus ABCD is a parallelogram

Thus, ABCD is a parallelogram.