https://file.aiquickdraw.com/mathbot/file/1727385136434732oiv24.jpg

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.

Given ABCD is a parallelogram. Prove: ∠A and ∠D are supplementary.

Learn how to prove that angles ∠A and ∠D in parallelogram ABCD are supplementary using the Same-Side Interior Angles Theorem. This problem is ideal for students in Grades 8-10 studying geometry and parallelogram properties.

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