Question

1. essential question what angle relationships are created when parallel lines are intersected by a transversal?

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Explanation:

When parallel lines are cut by a transversal, specific pairs of angles have equal or supplementary measures. These are the key defined relationships:

1. Corresponding angles: Lie in matching positions on each parallel line relative to the transversal, and are congruent.
2. Alternate interior angles: Lie between the parallel lines, on opposite sides of the transversal, and are congruent.
3. Alternate exterior angles: Lie outside the parallel lines, on opposite sides of the transversal, and are congruent.
4. Consecutive (same-side) interior angles: Lie between the parallel lines, on the same side of the transversal, and are supplementary (sum to $180^\circ$).
5. Vertical angles: Formed by intersecting lines (the transversal with each parallel line), are opposite each other, and are congruent.

Answer:

When parallel lines are intersected by a transversal, the following angle relationships are created:

• Corresponding angles: Congruent (equal in measure)
• Alternate interior angles: Congruent
• Alternate exterior angles: Congruent
• Consecutive (same-side) interior angles: Supplementary (sum to $180^\circ$)
• Vertical angles: Congruent (formed by the transversal intersecting each parallel line)