Question

in the diagram, $overleftrightarrow{ab}paralleloverleftrightarrow{cd}$. which pair of angles can be proven congruent?
$angle eiacongangle kij$
$angle eiacongangle gji$
$angle gjbcongangle ikl$
$angle gjbcongangle jlk$

Explanation:

Step1: Recall angle - congruence rules for parallel lines

When two parallel lines \(AB\parallel CD\) are cut by transversals, corresponding angles are congruent.

Step2: Identify corresponding angles

\(\angle EIA\) and \(\angle GJI\) are corresponding angles. Corresponding angles formed by two parallel lines and a transversal are congruent.

Step3: Analyze other options

• \(\angle EIA\) and \(\angle KIJ\) are vertical - angles, not related to the parallel - line property.
• \(\angle GJB\) and \(\angle IKL\) have no direct relation based on parallel - line angle rules.
• \(\angle GJB\) and \(\angle JLK\) are not corresponding, alternate - interior, or alternate - exterior angles with respect to the parallel lines \(AB\) and \(CD\).

Answer:

\(\angle EIA\cong\angle GJI\)