Question

name: as mullins date: per: geometry unit 3: parallel & perpendicular lines 3.1 & 3.2 quiz: parallel lines, transversals, and special angle pairs use the figure below for questions 1 - 4. 1. name a plane parallel to plane adf. 2. name a segment parallel to bc. 3. name a segment parallel to eh. 4. name a segment skew to fe. using the diagram to the right for questions 5 - 9, classify the angle - pair relationship as corresponding, alternate interior, alternate exterior, consecutive (same - side) interior angles, or consecutive (same - side) exterior angles. then name the transversal that connects them. 5. ∠1 and ∠14 corresponding transversal 6. ∠4 and ∠10 alternate interior transversal 7. ∠6 and ∠14 transversal 8. ∠7 and ∠13 transversal 9. ∠13 and ∠15 transversal if l || m, identify the angle pair as congruent or supplementary. justify your reasoning by classifying the angle pair. angle pair congruent or supplementary? classify 10. ∠1 and ∠8 11. ∠5 and ∠6 12. ∠6 and ∠8 13. ∠2 and ∠3 14. ∠4 and ∠7 15. ∠3 and ∠6

Explanation:

Step1: Recall angle - pair relationships

Corresponding angles are in the same relative position with respect to the transversal and the parallel lines. Alternate interior angles are between the two parallel lines and on opposite sides of the transversal. Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal. Consecutive (same - side) interior angles are between the two parallel lines and on the same side of the transversal. Consecutive (same - side) exterior angles are outside the two parallel lines and on the same side of the transversal.

Step2: Analyze congruent and supplementary angle pairs

If two parallel lines are cut by a transversal, corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, and consecutive (same - side) interior angles are supplementary, consecutive (same - side) exterior angles are supplementary.

1. ∠2 and ∠14 are corresponding angles. The transversal is the line that intersects the other two lines.
2. ∠4 and ∠10 are alternate interior angles. The transversal is the line that intersects the other two lines.
3. ∠6 and ∠14 are alternate exterior angles. The transversal is the line that intersects the other two lines.
4. ∠7 and ∠13 are consecutive (same - side) interior angles. The transversal is the line that intersects the other two lines.
5. ∠13 and ∠15 are consecutive (same - side) exterior angles. The transversal is the line that intersects the other two lines.

1. If \(l\parallel m\), for ∠1 and ∠8:

• They are alternate exterior angles.
• Since \(l\parallel m\), they are congruent.

1. For ∠5 and ∠6:

• They are consecutive (same - side) interior angles.
• Since \(l\parallel m\), they are supplementary.

1. For ∠6 and ∠8:

• They are vertical angles.
• Vertical angles are congruent.

1. For ∠2 and ∠3:

• They are adjacent angles that form a linear - pair.
• They are supplementary.

1. For ∠4 and ∠7:

• They are alternate interior angles.
• Since \(l\parallel m\), they are congruent.

1. For ∠3 and ∠6:

• They are corresponding angles.
• Since \(l\parallel m\), they are congruent.

Answer:

1. Corresponding, Transversal: [line name from the diagram]; 6. Alternate interior, Transversal: [line name from the diagram]; 7. Alternate exterior, Transversal: [line name from the diagram]; 8. Consecutive (same - side) interior, Transversal: [line name from the diagram]; 9. Consecutive (same - side) exterior, Transversal: [line name from the diagram]; 10. Congruent, Alternate exterior; 11. Supplementary, Consecutive (same - side) interior; 12. Congruent, Vertical angles; 13. Supplementary, Linear - pair; 14. Congruent, Alternate interior; 15. Congruent, Corresponding.