The image explains a proof of part of the Supplementary Consecutive Angles Theorem for a parallelogram, specifically proving that ∠A and ∠D are supplementary.

The key steps in the proof can be broken down as follows:

1. Given: $ABCD$ is a parallelogram.
2. To Prove: ∠A and ∠D are supplementary.

Proof Outline:

• Since $ABCD$ is a parallelogram, opposite sides $AB$ and $DC$ are parallel.
• $AD$ is a transversal across these parallel sides.
• By the properties of transversals and parallel lines, ∠A and ∠D are same-side interior angles.
• By the Same-Side Interior Angles Theorem, same-side interior angles are supplementary when a transversal intersects two parallel lines.
• Therefore, ∠A and ∠D must sum up to 180° (i.e., they are supplementary).

Would you like further clarification on any part of this proof?

Relative Questions:

1. What is the Same-Side Interior Angles Theorem?
2. How can you prove opposite sides in a parallelogram are parallel?
3. What are the other properties of parallelograms that help in geometric proofs?
4. Can you apply this theorem to non-parallelograms? Why or why not?
5. How can you use angle properties to determine unknown angles in polygons?

Tip:

When dealing with parallel lines and transversals, always look for angle relationships such as corresponding, alternate interior, or same-side interior angles to find supplementary or congruent angles.