Question

the figure shows a transversal that intersects two parallel lines. none of the angles are right angles. decide whether each pair of angles is congruent or not congruent. angles: ∠2 and ∠5, congruent or not congruent: not congruent; angles: ∠2 and ∠7, congruent or not congruent: congruent; angles: ∠4 and ∠8, congruent or not congruent: congruent; angles: ∠3 and ∠8, congruent or not congruent: ?

Explanation:

Step1: Recall angle relations with parallel lines and transversal

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 interior angles are supplementary. Vertical angles are also congruent.

Step2: Analyze ∠3 and ∠8

• First, ∠3 and ∠2 are vertical angles, so ∠3 = ∠2.
• We know from the table that ∠2 and ∠5 are not congruent, and ∠5 and ∠8 are vertical angles (∠5 = ∠8).
• Since ∠3 = ∠2 and ∠2 is not congruent to ∠5 (and ∠5 = ∠8), we can conclude that ∠3 and ∠8 are not congruent.

Answer:

not congruent