Chapter 5, Problem 15CT

To determine

To prove: that $ABCD$ is a parallelogram.

Explanation of Solution

Given information:

Given figure,

  

Given:

  $\overline{AB},\overline{BC},\overline{CD},$ and $\overline{DA}$ are all congruent.

Calculation:

Consider the given information,

  $\overline{AB},\overline{BC},\overline{CD},$ and $\overline{DA}$ 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.

Hence, quadrilateral $ABCD$ is either square or rhombus.

From the above facts as every square as well as every rhombus is a parallelogram therefore quadrilateral $ABCD$ is a parallelogram.

Hence, quadrilateral $ABCD$ is a parallelogram.