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Chapter 5: Q. 15 (page 199)

For the following figure, can you deduce from the information “AB¯,BC¯,CD¯ andDA¯ are all congruent” that quadrilateral ABCD is a parallelogram. If so, what theorem can you use?

Short Answer

Expert verified

The quadrilateral ABCD is a parallelogram.

Step by step solution

01

Step 1- Check the figure.

Consider the figure.

02

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.

03

Step 3- Step description.

Consider AD¯,BC¯,CD¯,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.

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Most popular questions from this chapter

What values must x and y have to make the quadrilateral a parallelogram?

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

Quadrilateral is a parallelogram.

  1. Why is supplementary to ?
  2. Why is supplementary to ?
  3. Complete: consecutive angles of a parallelogram are ?, while opposite angles are?.

Given:▱PQRS;localid="1637659881844" PJ¯≅RK¯

Prove: localid="1637659923835" SJ¯≅QK¯

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.
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