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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 180)

Points A, B, E and F are midpoints of $\bar{X C}, \bar{X D}, \bar{Y C}$ and $\bar{Y D}$ . Complete.
If $AB = 5 x - 8$ , and $EF = 3 x$ then $x =$ ? .

Short Answer

Expert verified

$x = 4$

Step by step solution

01

Step 1. Consider the diagram.

Here, A, B, E and F are the midpoints of sides $\bar{X C}, \bar{X D}, \bar{Y C}$ and $\bar{Y D}$ respectively.

And $A B = 5 x - 8$ and $E F = 3 x$ .

02

Step 2. Show the calculation.

Consider the triangle $△ X C D$ .

Here, points A and B are the midpoints of $\bar{X C}$ and $\bar{X D}$ .

So, by theorem 5-11 part (2), the side $\bar{A B}$ is half as long as the third side $\bar{C D}$ .

$A B = \frac{1}{2} C D$ …… (1)

Consider the triangle $△ Y C D$ .

Here, points E and F are the midpoints of $\bar{Y C}$ and $\bar{Y D}$ .

So, by theorem 5-11 part (2), the side $\bar{E F}$ is half as long as the third side $\bar{C D}$ .

$E F = \frac{1}{2} C D$ …… (2)

From (1) and (2),

$A B = E F$

Substitute $A B = 5 x - 8$ and $E F = 3 x$ .

$\begin{matrix} 5 x - 8 = 3 x \\ 5 x - 3 x = 8 \\ 2 x = 8 \\ x = 4 \end{matrix}$

03

Step 3. State the conclusion.

Therefore, $x = 4$ .

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Most popular questions from this chapter

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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