for use with the lesson \identify points, lines, and planes\ use the diagram to decide whether the given statement is true or false. 1. points h, i, and g are collinear. 2. points h, i, and j are coplanar. 3. $overrightarrow{eg}$ and $overrightarrow{fg}$ are opposite rays. 4. all points on $overrightarrow{gi}$ and $overrightarrow{gf}$ are coplanar. 5. the intersection of $overleftrightarrow{ef}$ and plane jkh is $overleftrightarrow{hi}$. 6. the intersection of $overleftrightarrow{ef}$, $overleftrightarrow{hi}$, and $overleftrightarrow{jg}$ is point g. 7. the intersection of plane egh and plane jgi is point g. 8. the intersection of plane efi and plane jkg is $overleftrightarrow{hg}$.

Question

Accepted Answer

### 1. Points $ H $, $ I $, and $ G $ are collinear.
# Answer:
False
# Explanation:
## Step1: Recall collinear definition
Collinear points lie on the same line.
## Step2: Analyze diagram
From the diagram, $ H $, $ G $, $ I $ do not lie on a single straight line (they are in different planes or positions not forming a line). So the statement is false.

### 2. Points $ H $, $ I $, and $ J $ are coplanar.
# Answer:
True
# Explanation:
## Step1: Recall coplanar definition
Coplanar points lie on the same plane.
## Step2: Analyze diagram
Points $ H $, $ I $, $ J $ lie on the plane that contains the line $ HI $ and the line $ JG $ (the vertical plane and the horizontal plane intersect, and these points are on the intersection - related plane or a common plane). So they are coplanar, statement is true.

### 3. $ \overrightarrow{EG} $ and $ \overrightarrow{FG} $ are opposite rays.
# Answer:
True
# Explanation:
## Step1: Recall opposite rays definition
Opposite rays have the same endpoint and form a straight line (are collinear and extend in opposite directions).
## Step2: Analyze diagram
$ \overrightarrow{EG} $ and $ \overrightarrow{FG} $ have the same endpoint $ G $ and lie on the straight line $ EF $, extending in opposite directions. So they are opposite rays, statement is true.

### 4. All points on $ \overrightarrow{GI} $ and $ \overrightarrow{GF} $ are coplanar.
# Answer:
True
# Explanation:
## Step1: Recall coplanar for lines
If two lines intersect, all points on them are coplanar (lie on the plane formed by the two lines).
## Step2: Analyze diagram
$ \overrightarrow{GI} $ and $ \overrightarrow{GF} $ intersect at $ G $. So all points on these two rays lie on the plane formed by them. Statement is true.

### 5. The intersection of $ \overleftrightarrow{EF} $ and plane $ JKH $ is $ \overleftrightarrow{HI} $.
# Answer:
False
# Explanation:
## Step1: Recall intersection of line and plane
The intersection of a line and a plane is a point (if the line is not in the plane) or the line itself (if the line is in the plane).
## Step2: Analyze diagram
$ \overleftrightarrow{EF} $ and plane $ JKH $ intersect at point $ G $ (or $ H $? Wait, from the diagram, $ \overleftrightarrow{EF} $ is horizontal, plane $ JKH $ is vertical. Their intersection is a point (probably $ G $ or $ H $), not $ \overleftrightarrow{HI} $. So statement is false.

### 6. The intersection of $ \overleftrightarrow{EF} $, $ \overleftrightarrow{HI} $, and $ \overrightarrow{JG} $ is point $ G $.
# Answer:
True
# Explanation:
## Step1: Recall intersection of multiple lines
The intersection of three lines is a point that lies on all three lines.
## Step2: Analyze diagram
$ \overleftrightarrow{EF} $, $ \overleftrightarrow{HI} $, and $ \overrightarrow{JG} $ all pass through point $ G $. So their intersection is $ G $, statement is true.

### 7. The intersection of plane $ EGH $ and plane $ JGI $ is point $ G $.
# Answer:
False
# Explanation:
## Step1: Recall intersection of two planes
The intersection of two planes is a line (if they are not parallel).
## Step2: Analyze diagram
Plane $ EGH $ and plane $ JGI $ intersect along a line (probably the line containing $ G $ and the vertical/horizontal line), not just a point. So statement is false.

### 8. The intersection of plane $ EFI $ and plane $ JKG $ is $ \overleftrightarrow{HG} $.
# Answer:
False
# Explanation:
## Step1: Recall intersection of two planes
The intersection of two planes is a line. We need to see the common line.
## Step2: Analyze diagram
Plane $ EFI $ and plane $ JKG $ intersect along a line (probably $ \overleftrightarrow{JG} $ or another line), not $ \overleftrightarrow{HG} $. So statement is false.

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QUESTION IMAGE

Question

Explanation:

1. Points \( H \), \( I \), and \( G \) are collinear.

Step1: Recall collinear definition

Step2: Analyze diagram

2. Points \( H \), \( I \), and \( J \) are coplanar.

Step1: Recall coplanar definition

Step2: Analyze diagram

3. \( \overrightarrow{EG} \) and \( \overrightarrow{FG} \) are opposite rays.

Step1: Recall opposite rays definition

Step2: Analyze diagram

4. All points on \( \overrightarrow{GI} \) and \( \overrightarrow{GF} \) are coplanar.

Answer: