Question

geometry
segment and angle practice 2025
name the vertex and sides of each angle:

1. diagram 2) diagram

name each angle in four ways.

1. diagram 4) diagram

name all the angles that have v as a vertex.

1. diagram 6) diagram

state if the given point is interior, exterior, or on the angle.

1. diagram 8) diagram

Explanation:

Problem 1: Name the vertex and sides of the angle

Step 1: Identify the vertex

The vertex of an angle is the common endpoint of the two rays forming the angle. In the first diagram, the common point is \( H \).

Step 2: Identify the sides

The sides are the two rays. Here, the rays are \( \overrightarrow{HJ} \) (or \( \overleftrightarrow{HJ} \) if it’s a segment) and \( \overrightarrow{HK} \).

Problem 2: Name the vertex and sides of the angle

Step 1: Identify the vertex

The common endpoint is \( K \).

Step 2: Identify the sides

The rays are \( \overrightarrow{KL} \) and \( \overrightarrow{KA} \).

Problem 3: Name the angle in four ways

Step 1: Using the vertex

The vertex is \( A \), so \( \angle A \).

Step 2: Using three points (middle is vertex)

The angle is formed by \( E \), \( A \), \( G \), so \( \angle EAG \), \( \angle GAE \).

Step 3: Using the vertex and a number (if labeled, but here we assume standard)

If the angle is labeled (e.g., with a number), but since it’s not, we use the three - point names and the vertex name. Wait, actually, for an angle with vertex \( A \), sides \( \overrightarrow{AE} \) and \( \overrightarrow{AG} \), the four ways are:

1. \( \angle A \)
2. \( \angle EAG \)
3. \( \angle GAE \)
4. If there was a number, but since not, maybe the problem expects using the vertex and the two rays’ labels. So \( \angle FAE \) (wait, the diagram has \( E \), \( A \), \( F \) and \( G \)? Wait, the diagram for 3 is \( E - A - F \) with a ray up to \( G \) from \( A \). So the angle is between \( \overrightarrow{AE} \) and \( \overrightarrow{AG} \). So four ways:

• \( \angle A \)
• \( \angle EAG \)
• \( \angle GAE \)
• \( \angle FAG \) (assuming \( F \) is on the same line as \( E - A \))

Problem 4: Name the angle in four ways

The vertex is \( J \), sides are \( \overrightarrow{JI} \) and \( \overrightarrow{JK} \). So four ways:

1. \( \angle J \)
2. \( \angle IJK \)
3. \( \angle KJI \)
4. If there was a number (e.g., \( \angle \alpha \) as in the diagram), \( \angle \alpha \)

Problem 5: Name all angles with vertex \( V \)

The rays from \( V \) are \( \overrightarrow{VH} \), \( \overrightarrow{VI} \), \( \overrightarrow{VJ} \). So the angles are:

• \( \angle HV I \) (between \( \overrightarrow{VH} \) and \( \overrightarrow{VI} \))
• \( \angle IVJ \) (between \( \overrightarrow{VI} \) and \( \overrightarrow{VJ} \))
• \( \angle HVJ \) (between \( \overrightarrow{VH} \) and \( \overrightarrow{VJ} \))

Problem 6: Name all angles with vertex \( V \)

The rays from \( V \) are \( \overrightarrow{VK} \), \( \overrightarrow{VJ} \), \( \overrightarrow{VI} \). So the angles are:

• \( \angle KVJ \) (between \( \overrightarrow{VK} \) and \( \overrightarrow{VJ} \))
• \( \angle JVI \) (between \( \overrightarrow{VJ} \) and \( \overrightarrow{VI} \))
• \( \angle KVI \) (between \( \overrightarrow{VK} \) and \( \overrightarrow{VI} \))

Problem 7: State if point \( P \) is interior, exterior, or on the angle

The angle has two sides. Point \( P \) is outside the region between the two sides of the angle, so it is exterior to the angle.

Problem 8: State if point \( P \) is interior, exterior, or on the angle

Point \( P \) lies on one of the sides (the ray) of the angle, so it is on the angle.

Answer:

s (for each sub - problem):

1. Vertex: \( H \); Sides: \( \overrightarrow{HJ} \), \( \overrightarrow{HK} \)
2. Vertex: \( K \); Sides: \( \overrightarrow{KL} \), \( \overrightarrow{KA} \)
3. Four names: \( \angle A \), \( \angle EAG \), \( \angle GAE \), \( \angle FAG \) (or other valid three - point combinations)
4. Four names: \( \angle J \), \( \angle IJK \), \( \angle KJI \), \( \angle \alpha \) (if \( \alpha \) is the angle label)
5. Angles: \( \angle HV I \), \( \angle IVJ \), \( \angle HVJ \)
6. Angles: \( \angle KVJ \), \( \angle JVI \), \( \angle KVI \)
7. Point \( P \): Exterior
8. Point \( P \): On the angle