Two lines in a plane are cut by a transversal .Which condition does NOT imply that the two lines are parallel ?

Options

A. A pair of alternate interior angles are congruent .
B. A pair of co- interior angles are supplementary .
C. A pair of corresponding angles are congruent .
D. A pair of alternate exterior angles are complementary .

Answer

To solve the question, we need to identify which condition does NOT imply that two lines cut by a transversal are parallel. Let's analyze the conditions one by one.

### Step-by-Step Solution:

1. **Understanding the Terms**:
- **Transversal**: A line that intersects two or more lines in a plane.
- **Parallel Lines**: Two lines that never meet and are always the same distance apart.
- **Angles**: Various types of angles formed when a transversal cuts two lines, such as alternate interior angles, co-interior angles, corresponding angles, and alternate exterior angles.

2. **Condition 1: Alternate Interior Angles are Congruent**:
- If a pair of alternate interior angles are equal, then the two lines are parallel.
- Example: If ∠AGH = ∠GHD, then AB || CD.
- **Conclusion**: This condition implies that the lines are parallel.

3. **Condition 2: Co-Interior Angles are Supplementary**:
- If a pair of co-interior angles are supplementary (sum to 180 degrees), then the two lines are parallel.
- Example: If ∠BGH + ∠GHD = 180°, then AB || CD.
- **Conclusion**: This condition implies that the lines are parallel.

4. **Condition 3: Corresponding Angles are Congruent**:
- If a pair of corresponding angles are equal, then the two lines are parallel.
- Example: If ∠EGB = ∠GHD, then AB || CD.
- **Conclusion**: This condition implies that the lines are parallel.

5. **Condition 4: Alternate Exterior Angles are Complementary**:
- If a pair of alternate exterior angles are complementary (sum to 90 degrees), this does NOT imply that the two lines are parallel.
- Example: If ∠AGE + ∠FHD = 90°, it does not guarantee that AB || CD.
- **Conclusion**: This condition does NOT imply that the lines are parallel.

### Final Answer:
The condition that does NOT imply that the two lines are parallel is: **A pair of alternate exterior angles are complementary.**

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