Questions: 3. Using CD as the transversal, which angles are considered alternate exterior angles? - angle CAQ and angle DBO - angle CAB and angle UBO - angle QAB and angle ABO - angle AQU and angle BOR 4. Why are the alternate interior angles, the alternate exterior angles, and the corresponding angles equal in this model? - Since the shape is a parallelogram the transversal must cross two parallel lines. - Since the shape is a parallelogram the transversal must cross two perpendicular lines. - The angles are not equal they are all supplementary. 5. Critical Thinking Problem: Which of the following segments is NOT considered a transversal? - CD - Qu - RO - CA

To address the question, let's focus on the first three parts as per the guidelines:

3. Using \( CD \) as the transversal, which angles are considered alternate exterior angles?

• \(\angle C A Q\) and \(\angle D B O\): These angles are on opposite sides of the transversal \( CD \) and outside the lines it intersects, making them alternate exterior angles.
• \(\angle C A B\) and \(\angle U B O\): These angles are not alternate exterior angles because they are not both outside the lines intersected by the transversal.
• \(\angle Q A B\) and \(\angle A B O\): These angles are not alternate exterior angles because they are not both outside the lines intersected by the transversal.
• \(\angle A Q U\) and \(\angle B O R\): These angles are not alternate exterior angles because they are not both outside the lines intersected by the transversal.

The answer is the first one: \(\angle C A Q\) and \(\angle D B O\).

4. Why are the alternate interior angles, the alternate exterior angles, and the corresponding angles equal in this model?

• Since the shape is a parallelogram the transversal must cross two parallel lines.: This is correct. In a parallelogram, opposite sides are parallel, and a transversal crossing these parallel lines creates equal alternate interior, alternate exterior, and corresponding angles.
• Since the shape is a parallelogram the transversal must cross two perpendicular lines.: This is incorrect because a parallelogram does not necessarily have perpendicular sides.
• The angles are not equal they are all supplementary.: This is incorrect in the context of parallel lines and a transversal, where alternate interior, alternate exterior, and corresponding angles are equal, not supplementary.

The answer is the first one: Since the shape is a parallelogram the transversal must cross two parallel lines.

5. Critical Thinking Problem: Which of the following segments is NOT considered a transversal?

• \( CD \): This is a transversal as it is mentioned in the context of the problem.
• \( QU \): This could be a transversal if it crosses two lines, but without additional context, it's unclear.
• \( RO \): This could be a transversal if it crosses two lines, but without additional context, it's unclear.
• \( CA \): This is likely not a transversal if it is one of the lines being intersected by the transversal \( CD \).

The answer is likely \( CA \), as it is not described as a transversal in the context provided.

In summary, the answers are: 3. \(\angle C A Q\) and \(\angle D B O\) 4. Since the shape is a parallelogram the transversal must cross two parallel lines. 5. \( CA \) is not considered a transversal.