Question

bd and eg are parallel lines. which angles are corresponding angles? ∠bcf and ∠gfh ∠bcf and ∠efh ∠bcf and ∠dca ∠bcf and ∠bca

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are angles that are in the same relative position with respect to the parallel lines and the transversal.

Step2: Analyze each option

• For \(\angle BCF\) and \(\angle GFH\):

Since \(\overleftrightarrow{BD}\parallel\overleftrightarrow{EG}\) and \(\overleftrightarrow{AH}\) is a transversal. \(\angle BCF\) and \(\angle GFH\) are in the same relative position (both are on the same - side of the transversal and in the "corner" positions relative to the parallel lines).

• For \(\angle BCF\) and \(\angle EFH\): They do not have the same relative position as required for corresponding angles.
• For \(\angle BCF\) and \(\angle DCA\): These are vertical angles (formed by the intersection of two lines \(BD\) and \(AH\)), not corresponding angles.
• For \(\angle BCF\) and \(\angle BCA\): These are adjacent angles, not corresponding angles.

Answer:

\(\angle BCF\) and \(\angle GFH\)