2:33 PM Wed Feb 19 $$ 17 \% $$ mylabschool.pearson.com ChatGP $$ { }^{-} $$ Max Headro... Encore: The... The Mystery... Enter Game... parallel lines... Geometry Period 11 Mckennah Person 02/19/25 2:33 PM This quiz: 23 point(s) $$ \equiv $$ Quiz: parallel lines chapter quiz Question 4 of 23 possible This question: 1 Submit quiz point(s) possible Question list Question 1 Question 2 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 The distinct lines a, b, c, and d are in the same plane. Tell how a and d relate. Justify your answer. $$ \mathrm{a} \perp \mathrm{~b}, \mathrm{~b}\|\mathrm{c}, \mathrm{c}\| \mathrm{d} $$ Choose the correct answer below. A. a is perpendicular to d because a is parallel to c and c is parallel to d . B. $$ a $$ is parallel to $$ d $$ because $$ a $$ is parallel to $$ c $$ and $$ c $$ is parallel to $$ d $$. C. a is perpendicular to d because a is perpendicular to c and c is parallel to d . D. $$ a $$ is parallel to $$ d $$ because $$ a $$ is perpendicular to $$ c $$ and $$ c $$ is parallel to $$ d $$.

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UpStudy AI · Accepted Answer

To determine how lines $$ a $$ and $$ d $$ relate, we need to analyze the given information about the relationships between the lines $$ a $$, $$ b $$, $$ c $$, and $$ d $$.

Given:
- $$ a \perp b $$ (line $$ a $$ is perpendicular to line $$ b $$)
- $$ b \parallel c $$ (line $$ b $$ is parallel to line $$ c $$)
- $$ c \parallel d $$ (line $$ c $$ is parallel to line $$ d $$)

From the given information, we can conclude the following:
- Since $$ a \perp b $$, line $$ a $$ is perpendicular to line $$ b $$.
- Since $$ b \parallel c $$, line $$ b $$ is parallel to line $$ c $$.
- Since $$ c \parallel d $$, line $$ c $$ is parallel to line $$ d $$.

Now, we need to determine the relationship between lines $$ a $$ and $$ d $$ based on the given information.

Let's analyze the options provided:
A. $$ a $$ is perpendicular to $$ d $$ because $$ a $$ is parallel to $$ c $$ and $$ c $$ is parallel to $$ d $$.
B. $$ a $$ is parallel to $$ d $$ because $$ a $$ is parallel to $$ c $$ and $$ c $$ is parallel to $$ d $$.
C. $$ a $$ is perpendicular to $$ d $$ because $$ a $$ is perpendicular to $$ c $$ and $$ c $$ is parallel to $$ d $$.
D. $$ a $$ is parallel to $$ d $$ because $$ a $$ is perpendicular to $$ c $$ and $$ c $$ is parallel to $$ d $$.

Based on the given information, we can see that lines $$ a $$ and $$ d $$ are parallel because $$ a $$ is parallel to $$ c $$ and $$ c $$ is parallel to $$ d $$. Therefore, the correct answer is:
B. $$ a $$ is parallel to $$ d $$ because $$ a $$ is parallel to $$ c $$ and $$ c $$ is parallel to $$ d $$.
Lines $$ a $$ and $$ d $$ are parallel because $$ a $$ is parallel to $$ c $$ and $$ c $$ is parallel to $$ d $$.

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