Question

lines \\(\overleftrightarrow{de}\\) and \\(\overleftrightarrow{ab}\\) are parallel.

image of two parallel lines with a transversal and a triangle

which angles represent alternate interior angles?

• angles a and c
• angles b and d
• angles c, d, and e
• angles b and c

Explanation:

Step1: Recall Alternate Interior Angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two parallel lines (interior) and on opposite sides of the transversal (alternate).

Step2: Analyze Each Option

• Option 1 (angles A and C): Angle A and C: Not alternate interior as they don't lie between the parallel lines with a transversal.
• Option 2 (angles B and D): Lines \( \overleftrightarrow{DE} \) and \( \overleftrightarrow{AB} \) are parallel, and the transversal is \( \overline{DB} \). Angles B and D lie between the parallel lines, on opposite sides of the transversal \( \overline{DB} \), so they are alternate interior angles.
• Option 3 (angles C, D, and E): These do not fit the alternate interior angle definition (not formed by a single transversal between two parallels in the required way).
• Option 4 (angles B and C): These are adjacent or not formed by a transversal between the parallels as alternate interior.

Answer:

B. angles B and D