Parallel Lines Cut by A Transversal: True/False | PDF - Free Printable

To solve the problem, we need to analyze the given diagram of parallel lines \( L \) and \( M \) intersected by a transversal \( N \). We will use properties of angles formed by parallel lines and a transversal to determine the truth or falsity of each statement.

Key Properties:

1. Corresponding Angles: Angles that are in the same relative position at each intersection. They are congruent.
2. Alternate Interior Angles: Angles on opposite sides of the transversal and between the two parallel lines. They are congruent.
3. Alternate Exterior Angles: Angles on opposite sides of the transversal and outside the two parallel lines. They are congruent.
4. Same-Side Interior Angles: Angles on the same side of the transversal and between the two parallel lines. They are supplementary (sum to 180°).
5. Vertical Angles: Angles opposite each other when two lines cross. They are congruent.
6. Supplementary Angles: Angles that add up to 180°.

Given Information:

- Angle 1 is given as \( 125^\circ \).

Step-by-Step Analysis:

#### 1. Angles 1 and 3 are vertical angles.
- Vertical angles are opposite each other when two lines intersect.
- Angles 1 and 3 are not opposite each other; they are adjacent.
- False

#### 2. The value of angle 7 is 125 degrees.
- Angles 1 and 7 are corresponding angles.
- Corresponding angles are congruent when the lines are parallel.
- Since angle 1 is \( 125^\circ \), angle 7 is also \( 125^\circ \).
- True

#### 3. Angles 1 and 6 are alternate interior angles.
- Alternate interior angles are on opposite sides of the transversal and between the parallel lines.
- Angles 1 and 6 are not between the parallel lines; they are on the same side.
- False

#### 4. Angles 3 and 5 are alternate interior angles.
- Angles 3 and 5 are on opposite sides of the transversal and between the parallel lines.
- Therefore, they are alternate interior angles.
- True

#### 5. Angles 4 and 8 are corresponding angles.
- Corresponding angles are in the same relative position at each intersection.
- Angles 4 and 8 are in the same relative position.
- True

#### 6. The value of angle 5 is 55 degrees.
- Angles 1 and 5 are same-side interior angles.
- Same-side interior angles are supplementary.
- Since angle 1 is \( 125^\circ \), angle 5 must be \( 180^\circ - 125^\circ = 55^\circ \).
- True

#### 7. Angles 1 and 7 are alternate exterior angles.
- Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines.
- Angles 1 and 7 are not outside the parallel lines; they are on the same side.
- False

#### 8. Angles 6 and 8 are corresponding angles.
- Corresponding angles are in the same relative position at each intersection.
- Angles 6 and 8 are in the same relative position.
- True

#### 9. Angles 1 and 6 are supplementary angles.
- Supplementary angles add up to 180°.
- Angles 1 and 6 are not supplementary; they are not adjacent and do not form a linear pair.
- False

#### 10. Angles 4 and 8 are supplementary angles.
- Angles 4 and 8 are corresponding angles, which means they are congruent.
- Corresponding angles are not supplementary unless they are both right angles (90°), which is not the case here.
- False

Final Answers:

1. False
2. True
3. False
4. True
5. True
6. True
7. False
8. True
9. False
10. False

\boxed{
\begin{array}{ll}
1. & \text{False} \\
2. & \text{True} \\
3. & \text{False} \\
4. & \text{True} \\
5. & \text{True} \\
6. & \text{True} \\
7. & \text{False} \\
8. & \text{True} \\
9. & \text{False} \\
10. & \text{False} \\
\end{array}
}