Question

bd and eg are parallel lines. which angles are corresponding angles? ∠bcf and ∠bca ∠bcf and ∠dcf ∠bcf and ∠efc ∠bcf and ∠efh

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are angles that are in the same relative position at each intersection where a straight line crosses two others. When two parallel lines are cut by a transversal, corresponding angles are equal.

Step2: Analyze each option

• Option 1: \(∠BCF\) and \(∠BCA\)

These angles are adjacent angles formed by two intersecting lines (\(BD\) and \(AH\)). They are not in the corresponding - angle position.

• Option 2: \(∠BCF\) and \(∠DCF\)

These are adjacent angles (they share a common side \(CF\) and a common vertex \(C\)). They are not corresponding angles.

• Option 3: \(∠BCF\) and \(∠EFC\)

These are alternate - interior angles (formed by the parallel lines \(BD\) and \(EG\) and the transversal \(AH\)). They are not in the corresponding - angle position.

• Option 4: \(∠BCF\) and \(∠EFH\)

Since \(\overleftrightarrow{BD}\parallel\overleftrightarrow{EG}\) and \(\overleftrightarrow{AH}\) is a transversal. \(∠BCF\) and \(∠EFH\) are in the same relative position (both are on the same side of the transversal \(AH\) and above the parallel lines \(BD\) and \(EG\) respectively).

Answer:

\(\angle BCF\) and \(\angle EFH\)