John’s classmate says that AB←→∥ DC←→
 based on the diagram shown.
 


Which of the following justifies his claim?
A.If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
B.If two lines and a transversal form same side interior angles that are supplementary, then the lines are parallel.
C.If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel.
D.If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel.


The correct justification for John's classmate's claim that \( AB \parallel DC \) (AB is parallel to DC) depends on the specific angle relationship given by the transversal cutting the two lines.

Each option relates to a specific type of angle pair created when two lines are cut by a transversal. Let's briefly analyze each choice:

- **A.** If two lines and a transversal form *corresponding angles* that are congruent, then the lines are parallel.  
- **B.** If two lines and a transversal form *same-side interior angles* that are supplementary, then the lines are parallel.  
- **C.** If two lines and a transversal form *alternate interior angles* that are congruent, then the lines are parallel.  
- **D.** If two lines and a transversal form *alternate exterior angles* that are congruent, then the lines are parallel.

Since all of these statements are valid theorems for determining if two lines are parallel, the specific one that justifies John's classmate’s claim depends on what kind of angles are provided by the diagram (which is missing in this case).

However, if we assume the most common case for parallel lines and transversals, **alternate interior angles** are often used to prove lines are parallel. Thus, the most likely answer is:

**C. If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel.**

Let me know if you need further clarification or have any questions!

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**Related Questions:**
1. How can you identify alternate interior angles in a diagram with parallel lines and a transversal?
2. What are the properties of corresponding angles when two lines are parallel?
3. How are same-side interior angles related when two lines are parallel?
4. Can alternate exterior angles also be used to prove lines are parallel?
5. How do supplementary angles help in determining if lines are parallel?

**Tip:** Always remember that the transversal creates multiple types of angle relationships when it cuts across two lines. Identifying these relationships is key to determining whether the lines are parallel.

John’s classmate says that AB←→∥ DC←→ based on the diagram shown. Which of the following justifies his claim? A. If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel. B. If two lines and a transversal form same side interior angles that are supplementary, then the lines are parallel. C. If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel. D. If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel.

Discover how to justify whether two lines are parallel using angle theorems. Learn about the corresponding angles, same-side interior angles, alternate interior angles, and alternate exterior angles when a transversal cuts two lines. Suitable for students in Grades 8-10.

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