Question

When you know that two consecutive sides of a parallelogram are congruent, you can prove that the parallelogram is a rhombus. Draw a diagram and explain.

Short answer

The parallelogram is a rhombus.

Step-by-step solution

Step 1. Check the figure.

Draw the figure of a parallelogram with two congruent consecutive sides.

Step 2. Step description.

Here ABCD is a parallelogram.

Since the opposite sides of a parallelogram are parallel thus, $AB\parallel DC$.

The distance between the two parallel lines is equal $AB=DC$

Similarly, $AB\parallel DC$then such that $AB=DC$.

Step 3. Step description.

Similarly, $AB\parallel BC$then such that $AB=BC$.

Therefore, the parallelogram with congruent consecutive sides is a rhombus.