think of each segment in the diagram as part of a line. complete the statement with parallel, skew, or neither.
7) $overleftrightarrow{wz}$ and $overleftrightarrow{zr}$ are ?.
8) $overleftrightarrow{wz}$ and $overleftrightarrow{st}$ are ?.
9) $overleftrightarrow{qt}$ and $overleftrightarrow{ys}$ are ?.
10) plane wzr and plane syz are ?.
11) plane rqt and plane yxw are ?.

identify the angles that go with the following types. (give all angles for each type)
12) corresponding angles
13) alternate exterior angles
14) same-side interior angles
15) alternate interior angles

Question

think of each segment in the diagram as part of a line. complete the statement with parallel, skew, or neither.
7) $overleftrightarrow{wz}$ and $overleftrightarrow{zr}$ are ?.
8) $overleftrightarrow{wz}$ and $overleftrightarrow{st}$ are ?.
9) $overleftrightarrow{qt}$ and $overleftrightarrow{ys}$ are ?.
10) plane wzr and plane syz are ?.
11) plane rqt and plane yxw are ?.

identify the angles that go with the following types. (give all angles for each type)
12) corresponding angles
13) alternate exterior angles
14) same-side interior angles
15) alternate interior angles

Accepted Answer

### Question 7
# Explanation:
## Step1: Analyze the lines
$\overleftrightarrow{WZ}$ and $\overleftrightarrow{ZR}$ share a common point $Z$, so they are not parallel (parallel lines never meet) and not skew (skew lines are non - parallel and non - intersecting in different planes). They intersect at $Z$.
# Answer:
neither

### Question 8
# Explanation:
## Step1: Recall properties of a rectangular prism
In a rectangular prism, opposite edges are parallel. $\overleftrightarrow{WZ}$ and $\overleftrightarrow{ST}$ are opposite edges of the rectangular prism, so they are parallel.
# Answer:
parallel

### Question 9
# Explanation:
## Step1: Analyze the lines' positions
$\overleftrightarrow{QT}$ and $\overleftrightarrow{YS}$ are in different planes, they do not intersect and are not parallel. So they are skew lines.
# Answer:
skew

### Question 10
# Explanation:
## Step1: Analyze the planes
Plane $WZR$ and plane $SYZ$ share the line $\overleftrightarrow{WZ}$ (or $\overleftrightarrow{SZ}$), so they are not parallel (parallel planes never meet) and not skew (planes can't be skew). They intersect along the line $\overleftrightarrow{WZ}$.
# Answer:
neither (they intersect)

### Question 11
# Explanation:
## Step1: Recall properties of a rectangular prism's planes
Plane $RQT$ and plane $YXW$ are opposite faces of the rectangular prism, so they are parallel.
# Answer:
parallel

### Question 12 (Corresponding angles)
# Explanation:
## Step1: Recall the definition of corresponding angles
Corresponding angles are in the same position relative to the transversal and the parallel lines (assuming the lines cut by the transversal are parallel). Looking at the diagram:
- $\angle1$ and $\angle5$: same position (bottom - left relative to their intersections)
- $\angle2$ and $\angle6$: same position (bottom - right)
- $\angle3$ and $\angle7$: same position (top - right)
- $\angle4$ and $\angle8$: same position (top - left)
# Answer:
$\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$

### Question 13 (Alternate exterior angles)
# Explanation:
## Step1: Recall the definition of alternate exterior angles
Alternate exterior angles are on the outside of the two lines cut by the transversal and on opposite sides of the transversal.
- $\angle1$ and $\angle8$: $\angle1$ is outside the right - hand lines, $\angle8$ is outside the right - hand lines, and they are on opposite sides of the transversal.
- $\angle4$ and $\angle5$: $\angle4$ is outside the left - hand lines, $\angle5$ is outside the left - hand lines, and they are on opposite sides of the transversal.
# Answer:
$\angle1$ and $\angle8$, $\angle4$ and $\angle5$

### Question 14 (Same - side interior angles)
# Explanation:
## Step1: Recall the definition of same - side interior angles
Same - side interior angles are on the same side of the transversal and inside the two lines cut by the transversal.
- $\angle3$ and $\angle5$: inside the two lines, same side of the transversal.
- $\angle2$ and $\angle8$: inside the two lines, same side of the transversal.
# Answer:
$\angle3$ and $\angle5$, $\angle2$ and $\angle8$

### Question 15 (Alternate interior angles)
# Explanation:
## Step1: Recall the definition of alternate interior angles
Alternate interior angles are on the inside of the two lines cut by the transversal and on opposite sides of the transversal.
- $\angle3$ and $\angle8$: inside the two lines, opposite sides of the transversal.
- $\angle2$ and $\angle5$: inside the two lines, opposite sides of the transversal.
# Answer:
$\angle3$ and $\angle8$, $\angle2$ and $\angle5$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 7

Step1: Analyze the lines

Step1: Recall properties of a rectangular prism

Step1: Analyze the lines' positions

Answer:

Question 8