1. **Problem statement:** We have three parallel lines cut by a transversal, with angles labeled as in the diagram. 2. **Part a:** Write a set of three corresponding angles that includes angle $f$. - Corresponding angles are pairs of angles that are in the same relative position at each intersection where a transversal crosses parallel lines. - Since $f$ is at the top-right of the middle intersection, the corresponding angles are $f$, $b$, and $j$ (top-right angles at each intersection). 3. **Part b:** Write a pair of alternate angles that includes angle $c$. - Alternate interior angles lie between the parallel lines and on opposite sides of the transversal. - Angle $c$ is bottom-right at the top intersection. - One alternate interior angle to $c$ is $h$ (bottom-left at the middle intersection). 4. **Part c:** Write another pair of alternate angles that includes angle $c$. - Another alternate angle to $c$ is $e$ (top-left at the middle intersection), which is alternate exterior to $c$. 5. **Part 8:** Determine whether pairs of angles are corresponding, alternate, or neither. - a) $a$ and $d$ are alternate interior angles. - b) $b$ and $f$ are corresponding angles. - c) $c$ and $g$ are alternate exterior angles. - d) $d$ and $e$ are neither corresponding nor alternate angles. - e) $a$ and $h$ are neither corresponding nor alternate angles. 6. **Part 9:** Arun's explanation that $h = b$ because they are corresponding angles, and $b = d$ because they are ... (likely alternate interior angles), shows the transitive property of equality for angles formed by parallel lines and a transversal. **Final answers:** - a) Corresponding angles including $f$: $\{f, b, j\}$ - b) Alternate angles including $c$: $c$ and $h$ - c) Another alternate pair including $c$: $c$ and $e$ - 8a) $a$ and $d$: alternate angles - 8b) $b$ and $f$: corresponding angles - 8c) $c$ and $g$: alternate angles - 8d) $d$ and $e$: neither - 8e) $a$ and $h$: neither $q_count = 1$