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Chapter 5: Q6 (page 186)

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

Expert verified

The parallelogram is a rhombus.

Step by step solution

01

Step 1. Check the figure.

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

02

Step 2. Step description.

Here ABCD is a parallelogram.

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

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

Similarly, AB∥DCthen such that AB=DC.

03

Step 3. Step description.

Similarly, AB∥BCthen such that AB=BC.

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

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Most popular questions from this chapter

Prove Theorem 5-2. (Draw and label a diagram. List what is given and what is to be proved.)

Prove Theorem 5-3.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

AD¯∥BC¯

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Draw a quadrilateral that isn’t a parallelogram but does have two 60°angles opposite each other.
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