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Chapter 5: Q5 (page 192)

Each diagram shows a trapezoid and its median. Find the value of x.

Short Answer

Expert verified

The value of x is 9.

Step by step solution

01

Step 1. Label the diagram.

02

Step 2. Apply the property of trapezoid.

The length of the median of the trapezoid is equal to the average length of the two bases.

From the given figure it can be observed that FC is the median and ABandEDare the two bases of the trapezoid. Therefore, the length of the median is given by

FC=12AB+ED

03

Step 3. Description of step.

Substitute 18 for AB, 8 for ED and x+4for FC into equation obtained in step 2 to find the value of x.

x+4=1218+8x+4=13x=13鈭�4=9

Therefore, the value of x is 9.

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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.

鈭�ADX鈮�鈭�CBX

For exercises, 14-18 write paragraph proofs.

Given: parallelogram ABCD; W, X, Y, Z are midpoints of AO炉, BO炉, CO炉and DO炉.

Prove: role="math" localid="1637745814874" WXYZ is a parallelogram.

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.

Must quad. EFGH be a parallelogram? Can it be a parallelogram? Explain.

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