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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

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 $ABandED$ are the two bases of the trapezoid. Therefore, the length of the median is given by

$F C = \frac{1}{2} (A B + E D)$

03

Step 3. Description of step.

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

$\begin{matrix} x + 4 = \frac{1}{2} (18 + 8) \\ x + 4 = 13 \\ x = 13 - 4 \\ = 9 \end{matrix}$

Therefore, the value of x is 9.

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Most popular questions from this chapter

State the principal definition or theorem that enables you to deduce, from the information given, that quadrilateral SACK is a parallelogram.

$\bar{SA} ∥ \bar{KC}$ ;role="math" localid="1637731683825" $\bar{SK} ∥ \bar{AC}$

Quad. DECK is a parallelogram. Complete.

If $KT = 2 x + y, DT = x + 2 y, TE = 12$ and $TC = 9$ , then $x = ?$ and $y = ?$

The pliers shown are made in such a way that the jaws are always parallel. Explain.

What values must x and y have to make the quadrilateral 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.

See all solutions

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