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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鈭�DC.

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

Similarly, AB鈭�DCthen such that AB=DC.

03

Step 3. Step description.

Similarly, AB鈭�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

For the following figure, if OE=4and WE=8, name two segments congruent to WE炉.

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

鈻�DECKis a parallelogram. Complete.

Ifm鈭�1=3x,m鈭�2=4x and m鈭�3=x2-70then x=?andm鈭�CED=? (numerical answers).

Given:鈻�PQRS;localid="1637659881844" PJ炉鈮�RK炉

Prove: localid="1637659923835" SJ炉鈮�QK炉

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

AD炉鈭�BC炉
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