Question

lines l and m are intersected by transversal t and l || m. which of the following angles are congruent to ∠5? select all that apply. a. ∠1 b. ∠2 c. ∠3 d. ∠4

Explanation:

Step1: Recall angle - congruence rules for parallel lines

When two parallel lines \(l\) and \(m\) are cut by a transversal \(t\), corresponding angles are congruent, alternate - interior angles are congruent, and vertical angles are congruent.

Step2: Identify corresponding and alternate - interior angles to \(\angle5\)

\(\angle1\) and \(\angle5\) are corresponding angles. Corresponding angles formed by two parallel lines and a transversal are congruent. So \(\angle1\cong\angle5\).
\(\angle4\) and \(\angle5\) are alternate - interior angles. Alternate - interior angles formed by two parallel lines and a transversal are congruent. So \(\angle4\cong\angle5\).
\(\angle2\) is not congruent to \(\angle5\) as they are neither corresponding, alternate - interior, nor vertical angles.
\(\angle3\) is not congruent to \(\angle5\) as they are neither corresponding, alternate - interior, nor vertical angles.

Answer:

A. \(\angle1\), D. \(\angle4\)