planes 11. how many points are needed to define a plane? (spcivt check) name the intersection of line $\overline{qz}$ and segment $\overline{wu}$. name the intersection of plane $\pi$ and line $\overline{db}$. name the two opposite rays at point t. what is another name for plane $\pi$?

Question

Accepted Answer

### 1. How many points are needed to define a plane?
# Explanation:
## Step1: Recall the geometric principle
In geometry, a fundamental principle states that a plane is defined by three non - collinear points. Non - collinear points are points that do not all lie on the same straight line. If we have three non - collinear points, there is exactly one plane that contains all three of them.
# Answer:
Three non - collinear points are needed to define a plane.

### 2. Name the intersection of line $\overleftrightarrow{QZ}$ and segment $\overline{WU}$.
# Explanation:
## Step1: Analyze the diagram
From the given diagram, we can see that line $\overleftrightarrow{QZ}$ and segment $\overline{WU}$ intersect at a point. By looking at the labels in the diagram, the point of intersection of line $\overleftrightarrow{QZ}$ and segment $\overline{WU}$ is point $T$.
# Answer:
The intersection of line $\overleftrightarrow{QZ}$ and segment $\overline{WU}$ is point $T$.

### 3. Name the intersection of plane $\pi$ and line $\overleftrightarrow{DB}$.
# Explanation:
## Step1: Recall the intersection of a plane and a line
The intersection of a plane and a line is either a point (if the line intersects the plane at one point) or the line itself (if the line lies on the plane). From the diagram, line $\overleftrightarrow{DB}$ lies on plane $\pi$ (since all the points of the line $\overleftrightarrow{DB}$ are within the plane $\pi$ as per the diagram). So the intersection of plane $\pi$ and line $\overleftrightarrow{DB}$ is the line $\overleftrightarrow{DB}$ itself.
# Answer:
The intersection of plane $\pi$ and line $\overleftrightarrow{DB}$ is line $\overleftrightarrow{DB}$.

### 4. Name the two opposite rays at point $T$.
# Explanation:
## Step1: Recall the definition of opposite rays
Opposite rays are two rays that have the same endpoint and form a straight line (a linear pair, so their sum of angles is $180^{\circ}$). For example, if we consider point $T$ as the endpoint, we can look at rays like $\overrightarrow{TQ}$ and $\overrightarrow{TZ}$ (since they have the same endpoint $T$ and form a straight line) or $\overrightarrow{TD}$ and $\overrightarrow{TB}$ (also with the same endpoint $T$ and forming a straight line) or $\overrightarrow{TW}$ and $\overrightarrow{TU}$ (same logic).
# Answer:
Two opposite rays at point $T$ can be $\overrightarrow{TQ}$ and $\overrightarrow{TZ}$ (or $\overrightarrow{TD}$ and $\overrightarrow{TB}$, or $\overrightarrow{TW}$ and $\overrightarrow{TU}$).

### 5. What is another name for plane $\pi$?
# Explanation:
## Step1: Recall the naming of planes
A plane can be named by three non - collinear points that lie on the plane. From the diagram, points like $W$, $U$, $Q$ (or other combinations of non - collinear points on the plane) can be used to name the plane. So another name for plane $\pi$ can be plane $WUQ$ (or plane formed by other three non - collinear points on the plane, like plane $WTD$ etc.).
# Answer:
Another name for plane $\pi$ is plane $WUQ$ (or other valid names using three non - collinear points on the plane).

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QUESTION IMAGE

Question

Explanation:

1. How many points are needed to define a plane?

Step1: Recall the geometric principle

Step1: Analyze the diagram

Step1: Recall the intersection of a plane and a line

Answer:

2. Name the intersection of line \(\overleftrightarrow{QZ}\) and segment \(\overline{WU}\).