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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: Q2 (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 $AB = k$ , then $C D = ?$ and $EF = ?$ .

Short Answer

Expert verified

$CD = 2 k$ and $EF = k$ .

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 $A B = k$

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 $\bar{C D}$ .

$A B = \frac{1}{2} C D$

So,

$\begin{matrix} C D = 2 A B \\ = 2 k \end{matrix}$

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 $\bar{C D}$ .

$\begin{matrix} E F = \frac{1}{2} C D \\ = \frac{1}{2} \times 2 k \\ = k \end{matrix}$

03

Step 3. State the conclusion.

Therefore, $\bar{C D} = 2 k$ and $\bar{E F} = k$ .

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Most popular questions from this chapter

In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

M, N and T are the midpoints of the sides of $Δ XYZ$ .

If $ZN = 8$ , then $TM = \underline{?}$

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

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

$∠ ADX ≅ ∠ CBX$

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

See all solutions

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