Question

quiz 3 - 1: parallel lines, transversals, and special angle pairs
per: 6
geometry unit 3: parallel & perpendicular lines
use the figure below for questions 1 - 4.

1. name a plane parallel to plane def.
2. name a segment parallel to (overline{fc}).
3. name a segment parallel to (overline{ab}).
4. name a segment skew to (overline{de}).

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, or consecutive (same - side) exterior angles. then, name the transversal that connects them.

1. (angle1) and (angle14)
2. (angle4) and (angle10)
3. (angle6) and (angle16)
4. (angle7) and (angle12)
5. (angle13) and (angle15)

if (lparallel m), identify the angle pair as congruent or supplementary. justify your reasoning by classifying the angle pair.
angle pair congruent or supplementary? classify

1. (angle1) and (angle8)
2. (angle5) and (angle6)
3. (angle6) and (angle8)
4. (angle2) and (angle3)
5. (angle4) and (angle7)
6. (angle3) and (angle6)

Explanation:

Step1: Recall angle - pair relationships

When 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.

Step2: Analyze each angle - pair

For ∠1 and ∠8

They are alternate exterior angles. Since l || m, alternate exterior angles are congruent. So the answer for 10 is: Congruent, Alternate exterior angle.

For ∠5 and ∠6

They are consecutive (same - side) interior angles. Since l || m, consecutive (same - side) interior angles are supplementary. So the answer for 11 is: Supplementary, Consecutive (same - side) interior angle.

For ∠6 and ∠8

They are consecutive (same - side) interior angles. Since l || m, consecutive (same - side) interior angles are supplementary. So the answer for 12 is: Supplementary, Consecutive (same - side) interior angle.

For ∠2 and ∠3

They are alternate interior angles. Since l || m, alternate interior angles are congruent. So the answer for 13 is: Congruent, Alternate interior angle.

For ∠4 and ∠7

They are consecutive (same - side) interior angles. Since l || m, consecutive (same - side) interior angles are supplementary. So the answer for 14 is: Supplementary, Consecutive (same - side) interior angle.

For ∠3 and ∠6

They are corresponding angles. Since l || m, corresponding angles are congruent. So the answer for 15 is: Congruent, Corresponding angle.

Answer:

1. Congruent, Alternate exterior angle
2. Supplementary, Consecutive (same - side) interior angle
3. Supplementary, Consecutive (same - side) interior angle
4. Congruent, Alternate interior angle
5. Supplementary, Consecutive (same - side) interior angle
6. Congruent, Corresponding angle