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Chapter 5: Q. 15 (page 199)

For the following figure, can you deduce from the information 鈥�AB炉,BC炉,CD炉 andDA炉 are all congruent鈥� 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炉,BC炉,CD炉,DA炉 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

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

DX=BX

Draw a quadrilateral that is not a parallelogram but that has one pair of congruent sides and one pair of parallel sides.

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-4.

Given: ABCD is a 鈻�,CD炉鈮�CE炉

Prove: 鈭�A鈮�鈭�E

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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