Solved ANGLES formed by a TRANSVERSAL ....... j 57 6/ 8 NAME ... - Free Printable

Problem Analysis:

The image shows two parallel lines \( j \) and \( k \) intersected by a transversal line \( m \). Various angles are labeled from 1 to 16. The task is to identify and name the relationships between specific pairs of angles formed by the transversal, as well as list examples of corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, and consecutive exterior angles.

Solution:

#### Step 1: Identify the Transversal Relationships
The transversal \( m \) intersects the parallel lines \( j \) and \( k \), creating several types of angle pairs. We will analyze each pair given in the problem:

1. ∠1 and ∠12:
- These angles are on the same side of the transversal and are outside the parallel lines.
- They are Consecutive (Same-Side) Exterior Angles.

2. ∠3 and ∠6:
- These angles are on opposite sides of the transversal and are inside the parallel lines.
- They are Alternate Interior Angles.

3. ∠7 and ∠15:
- These angles are on the same side of the transversal and are inside the parallel lines.
- They are Consecutive (Same-Side) Interior Angles.

4. ∠12 and ∠14:
- These angles are on opposite sides of the transversal and are outside the parallel lines.
- They are Alternate Exterior Angles.

#### Step 2: List Examples of Each Type of Angle Pair
Now, we will identify examples of each type of angle pair formed by the transversal:

1. Corresponding Angles:
- Corresponding angles are in the same relative position at each intersection.
- Examples:
- ∠1 and ∠9
- ∠2 and ∠10
- ∠3 and ∠11
- ∠4 and ∠12
- ∠5 and ∠13
- ∠6 and ∠14
- ∠7 and ∠15
- ∠8 and ∠16

2. Alternate Interior Angles:
- Alternate interior angles are on opposite sides of the transversal and inside the parallel lines.
- Examples:
- ∠3 and ∠6
- ∠4 and ∠5
- ∠11 and ∠14
- ∠12 and ∠13

3. Alternate Exterior Angles:
- Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines.
- Examples:
- ∠1 and ∠8
- ∠2 and ∠7
- ∠9 and ∠16
- ∠10 and ∠15

4. Consecutive (Same-Side) Interior Angles:
- Consecutive interior angles are on the same side of the transversal and inside the parallel lines.
- Examples:
- ∠3 and ∠5
- ∠4 and ∥6
- ∠11 and ∠13
- ∠12 and ∠14

5. Consecutive (Same-Side) Exterior Angles:
- Consecutive exterior angles are on the same side of the transversal and outside the parallel lines.
- Examples:
- ∠1 and ∠7
- ∠2 and ∠8
- ∠9 and ∠15
- ∠10 and ∠16

#### Step 3: Non-Examples
Non-examples are angle pairs that do not fit into any of the above categories. For example:
- ∠1 and ∠4 (adjacent angles)
- ∠5 and ∠10 (not related by the transversal in a standard way)

Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Name That Transversal:} & \\
\angle1 \text{ and } \angle12: & \text{Consecutive (Same-Side) Exterior Angles} \\
\angle3 \text{ and } \angle6: & \text{Alternate Interior Angles} \\
\angle7 \text{ and } \angle15: & \text{Consecutive (Same-Side) Interior Angles} \\
\angle12 \text{ and } \angle14: & \text{Alternate Exterior Angles} \\
\end{array}
}
\]

\[
\boxed{
\begin{array}{l}
\text{Corresponding Angles:} \\
\cdot \angle1 \text{ and } \angle9 \\
\cdot \angle2 \text{ and } \angle10 \\
\cdot \angle3 \text{ and } \angle11 \\
\cdot \angle4 \text{ and } \angle12 \\
\cdot \angle5 \text{ and } \angle13 \\
\cdot \angle6 \text{ and } \angle14 \\
\cdot \angle7 \text{ and } \angle15 \\
\cdot \angle8 \text{ and } \angle16 \\
\end{array}
}
\]

\[
\boxed{
\begin{array}{l}
\text{Alternate Interior Angles:} \\
\cdot \angle3 \text{ and } \angle6 \\
\cdot \angle4 \text{ and } \angle5 \\
\cdot \angle11 \text{ and } \angle14 \\
\cdot \angle12 \text{ and } \angle13 \\
\end{array}
}
\]

\[
\boxed{
\begin{array}{l}
\text{Alternate Exterior Angles:} \\
\cdot \angle1 \text{ and } \angle8 \\
\cdot \angle2 \text{ and } \angle7 \\
\cdot \angle9 \text{ and } \angle16 \\
\cdot \angle10 \text{ and } \angle15 \\
\end{array}
}
\]

\[
\boxed{
\begin{array}{l}
\text{Consecutive (Same-Side) Interior Angles:} \\
\cdot \angle3 \text{ and } \angle5 \\
\cdot \angle4 \text{ and } \angle6 \\
\cdot \angle11 \text{ and } \angle13 \\
\cdot \angle12 \text{ and } \angle14 \\
\end{array}
}
\]

\[
\boxed{
\begin{array}{l}
\text{Consecutive (Same-Side) Exterior Angles:} \\
\cdot \angle1 \text{ and } \angle7 \\
\cdot \angle2 \text{ and } \angle8 \\
\cdot \angle9 \text{ and } \angle15 \\
\cdot \angle10 \text{ and } \angle16 \\
\end{array}
}
\]