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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 3: Q9. (page 111)

Which line is parallel to $\bar{AB}$ ? Why?

Short Answer

Expert verified

The line $\bar{A B}$ is parallel to the line $\bar{DF}$ as they form a pair of same-side interior angles.

Step by step solution

01

Step 1. Highlight ∠BAD and ∠ADF.

02

Step 2. Description of step.

If a line intersects two lines and it makes two angles on the same side such that sum of two angles is equal to $180 °$ , then the lines are parallel and that line is a transversal of two parallel lines.

03

Step 3. Description of step.

From the figure, it can be observed that $∠ B A D$ and $∠ A D F$ are the same side interior angles, as

$\begin{array}{r} m ∠ B A D + m ∠ A D F = 115 + 65 \\ = 180 \end{array}$

Therefore, lines $\bar{A B}$ and $\bar{D F}$ are parallel.

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Most popular questions from this chapter

Complete each statement with the word always, sometimes, or never. Two skew lines are parallel.

Name the two lines and the transversal that form each pair of angles.

and

Write proof in two column form

Given: $k ∥ l$

Prove: $∠ 2 ≅ ∠ 7$

If $c ∥ d$ , name all angels that must be congruent to $∠ 1$ .

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