2:17 PM Wed Feb 19 $$ 21 \% $$ mylabschool.pearson.com ChatGP $$ { }^{-} $$ Max Headro... Encore: The... The Mystery... K! Kahoot! parallel lines... Geometry Period 11 Mckennah Person 02/19/25 2:17 PM This quiz: 23 point(s) $$ \equiv $$ Quiz: parallel lines chapter quiz Question 2 of 23 This question: 1 Submit quiz point(s) possible Question list Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 Question 11 Use the given information to determine which lines, if any, in the figure to the right are parallel. Justify each conclusion with a theorem or postulate. $$ \angle 2 $$ is supplementary to $$ \angle 3 $$. Fill in the blanks below. Because it is given that $$ \angle 2 $$ is supplementary to $$ \angle 3 $$, $$ \square $$ by the $$ \square $$ a || k a || b k || m b || k

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UpStudy AI · Accepted Answer

To determine which lines are parallel based on the given information that $$ \angle 2 $$ is supplementary to $$ \angle 3 $$, we can use the properties of angles formed by a transversal intersecting two lines.

### Step 1: Understand the Given Information
- We know that $$ \angle 2 $$ and $$ \angle 3 $$ are supplementary. This means:
$$
\angle 2 + \angle 3 = 180^\circ
$$

### Step 2: Identify the Relationships
- If two angles are supplementary and they are interior angles on the same side of a transversal, then the lines are parallel. This is known as the Consecutive Interior Angles Theorem.

### Step 3: Apply the Theorem
- Since $$ \angle 2 $$ is supplementary to $$ \angle 3 $$, we can conclude that if $$ \angle 2 $$ and $$ \angle 3 $$ are located between two lines (let's say lines $$ a $$ and $$ b $$), then:
$$
a \parallel b
$$

### Step 4: Fill in the Blanks
Based on the information and the theorem, we can fill in the blanks as follows:

- Because it is given that $$ \angle 2 $$ is supplementary to $$ \angle 3 $$, $$ a \parallel b $$ by the **Consecutive Interior Angles Theorem**.

### Conclusion
Thus, the answer is:
- **First Blank:** $$ a \parallel b $$
- **Second Blank:** **Consecutive Interior Angles Theorem**

If you have any specific lines or angles in the figure that you want to analyze further, please provide that information for a more detailed conclusion.
Because $$ \angle 2 $$ and $$ \angle 3 $$ are supplementary, lines $$ a $$ and $$ b $$ are parallel by the Consecutive Interior Angles Theorem.

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