15. what is true about the slopes of parallel lines?
16. what is true about the lines of perpendicular lines?
17. what are the 8 angles of a transversal line?
18. name all the 8 angles of the transversal lines of parallel lines.
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Question

Accepted Answer

### Question 15
# Explanation:
## Step1: Recall parallel lines slope property
Parallel lines have equal slopes. For two lines with slopes $m_1$ and $m_2$, if they are parallel, $m_1 = m_2$.
# Answer:
The slopes of parallel lines are equal.

### Question 16
# Explanation:
## Step1: Recall perpendicular lines slope property
For two non - vertical perpendicular lines with slopes $m_1$ and $m_2$, the product of their slopes is $- 1$, i.e., $m_1\times m_2=-1$. If one line is vertical (undefined slope) and the other is horizontal (slope = 0), they are also perpendicular.
# Answer:
The product of the slopes of two non - vertical perpendicular lines is $-1$ (or one line is vertical and the other is horizontal).

### Question 17
# Explanation:
## Step1: Define transversal and angles
A transversal is a line that intersects two or more other lines. When a transversal intersects two lines, it forms 8 angles: 4 angles at each intersection point. These angles include corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles (also known as same - side interior angles), along with vertical angles and linear pairs. But in terms of naming the 8 angles, we can consider the angles formed at each of the two intersection points. Let the two lines be $l_1$ and $l_2$ and the transversal be $t$. At the intersection of $t$ and $l_1$, we have $\angle1$, $\angle2$, $\angle3$, $\angle4$ (in order around the intersection), and at the intersection of $t$ and $l_2$, we have $\angle5$, $\angle6$, $\angle7$, $\angle8$ (in order around the intersection).
# Answer:
When a transversal intersects two lines, the 8 angles are formed at the two intersection points. At each intersection, there are 4 angles. We can name them as $\angle1$, $\angle2$, $\angle3$, $\angle4$ (at the first intersection) and $\angle5$, $\angle6$, $\angle7$, $\angle8$ (at the second intersection) (or using angle - pair names like corresponding, alternate etc.).

### Question 18
# Explanation:
## Step1: Recall transversal of parallel lines angle names
When a transversal intersects two parallel lines, the 8 angles are: 4 pairs of corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles, along with vertical angles and linear pairs. Specifically, if we have two parallel lines $l_1\parallel l_2$ and transversal $t$, the 8 angles can be named as follows: Corresponding angles (e.g., $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$), Alternate interior angles ($\angle3$ and $\angle6$, $\angle4$ and $\angle5$), Alternate exterior angles ($\angle1$ and $\angle8$, $\angle2$ and $\angle7$), Consecutive interior angles ($\angle3$ and $\angle5$, $\angle4$ and $\angle6$), and also vertical angles (e.g., $\angle1$ and $\angle3$, $\angle2$ and $\angle4$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$) and linear pairs (e.g., $\angle1$ and $\angle2$, $\angle2$ and $\angle3$ etc.). But in terms of naming all 8 angles, we can use a numbering system. Let the two parallel lines be $m$ and $n$ and the transversal be $p$. At the intersection of $p$ and $m$, the angles are $\angle1$ (top - left), $\angle2$ (top - right), $\angle3$ (bottom - right), $\angle4$ (bottom - left). At the intersection of $p$ and $n$, the angles are $\angle5$ (top - left), $\angle6$ (top - right), $\angle7$ (bottom - right), $\angle8$ (bottom - left).
# Answer:
The 8 angles formed by a transversal of parallel lines can be named (using a common numbering convention) as $\angle1$, $\angle2$, $\angle3$, $\angle4$ (at the intersection with the first parallel line) and $\angle5$, $\angle6$, $\angle7$, $\angle8$ (at the intersection with the second parallel line). These angles include corresponding angles ($\angle1$ & $\angle5$, $\angle2$ & $\angle6$, $\angle3$ & $\angle7$, $\angle4$ & $\angle8$), alternate interior angles ($\angle3$ & $\angle6$, $\angle4$ & $\angle5$), alternate exterior angles ($\angle1$ & $\angle8$, $\angle2$ & $\angle7$) and consecutive interior angles ($\angle3$ & $\angle5$, $\angle4$ & $\angle6$) along with vertical and linear - pair angles.

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QUESTION IMAGE

Question

Explanation:

Question 15

Step1: Recall parallel lines slope property

Step1: Recall perpendicular lines slope property

Step1: Define transversal and angles

Answer:

Question 16