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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: Q3 (page 192)

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

Short Answer

Expert verified

The value of x is 15.

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 ABand ED 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 x for AB, 7 for ED, and 11 for FC into the equation obtained in step 2 to find the value of x.

$\begin{matrix} 11 = \frac{1}{2} (x + 7) \\ 22 = x + 7 \\ x = 22 - 7 \\ = 15 \end{matrix}$

Therefore, the value of x is 15.

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Most popular questions from this chapter

Draw a quadrilateral that isn’t a parallelogram but does have two $60 °$ angles opposite each other.

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

$\bar{S A} ≅ \bar{K C}; \bar{S A} ∥ \bar{K C}$

For the following figure, if $\bar{W R} ⊥ \bar{C E}$ then name all segments congruent to $\bar{W E}$ .

Find something interesting to prove. Then prove it. Answers may vary.

Given: $▱ ABCD; ∠ 1 ≅ ∠ 2$

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

See all solutions

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