Question

section 3.1
i can identify parallel and perpendicular lines and pairs of angles.
use the figure below to answer #1 - 5

1. name a pair of parallel lines.
2. name a pair of perpendicular lines.
3. name a pair of corresponding angles (use the #s).
4. name a pair of alternate interior angles (use the #s).
5. classify ∠1 and ∠5 as corresponding, alternate

interior, alternate exterior, or consecutive interior.

Explanation:

Step1: Parallel lines identification

Parallel lines are lines that never intersect. In the figure, \(AD\) and \(EF\) are parallel as they are two straight lines that do not meet.

Step2: Perpendicular lines identification

Perpendicular lines form a right - angle (\(90^{\circ}\)). \(CF\) forms a right - angle with \(AD\) (and also with \(EF\) since \(AD\parallel EF\)).

Step3: Corresponding angles identification

Corresponding angles are in the same relative position. \(\angle2\) and \(\angle3\) are in the same relative position with respect to the transversal \(BG\) and the parallel lines \(AD\) and \(EF\).

Step4: Alternate interior angles identification

Alternate interior angles are between the two parallel lines and on opposite sides of the transversal. \(\angle2\) and \(\angle5\) are between \(AD\) and \(EF\) and on opposite sides of transversal \(BG\).

Step5: Classifying \(\angle1\) and \(\angle5\)

\(\angle1\) and \(\angle5\) are outside the two parallel lines (\(AD\) and \(EF\)) and on opposite sides of the transversal \(BG\), so they are alternate exterior angles.

Answer:

1. \(AD\parallel EF\)
2. \(CF\perp AD\) (or \(CF\perp EF\))
3. \(\angle2\) and \(\angle3\)
4. \(\angle2\) and \(\angle5\)
5. Alternate exterior angles