Question

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

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 $\angle BCA$: These are adjacent angles, not corresponding.
• For $\angle BCF$ and $\angle GFH$: $\angle BCF$ and $\angle GFH$ are in the same relative position (both are on the same side of the transversal and in the same "corner" relative to the parallel lines $BD$ and $EG$).
• For $\angle BCF$ and $\angle DCA$: These are vertical - opposite - like angles (vertically opposite at point $C$), not corresponding.
• For $\angle BCF$ and $\angle EFH$: These are not in the same relative position to be corresponding angles.

Answer:

$\angle BCF$ and $\angle GFH$