Question
Which diagram shows parallel lines cut by a transversal?
2 lines are cut by a transversal. At the intersection of the first line with the transversal, the uppercase left angle is 75 degrees. At the intersection of the second line with the transversal, the uppercase left angle is 80 degrees.
2 lines are cut by a transversal. At the intersection of the first line with the transversal, the bottom left angle is 85 degrees. At the intersection of the second line with the transversal, the uppercase right angle is 81 degrees.
2 lines are cut by a transversal. At the intersection of the first line with the transversal, the bottom right angle is 130 degrees. At the intersection of the second line with the transversal, the uppercase right angle is 50 degrees.
2 lines are cut by a transversal. At the intersection of the first line with the transversal, the uppercase left angle is 75 degrees. At the intersection of the second line with the transversal, the uppercase left angle is 80 degrees.
2 lines are cut by a transversal. At the intersection of the first line with the transversal, the bottom left angle is 85 degrees. At the intersection of the second line with the transversal, the uppercase right angle is 81 degrees.
2 lines are cut by a transversal. At the intersection of the first line with the transversal, the bottom right angle is 130 degrees. At the intersection of the second line with the transversal, the uppercase right angle is 50 degrees.
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Answered by
GPT-4o mini
To determine which diagram shows parallel lines cut by a transversal, we can use the properties of angles formed by a transversal crossing parallel lines. Specifically, when two parallel lines are cut by a transversal:
1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Same-side interior angles are supplementary (sum to 180 degrees).
Now, let's analyze each set of angles given in your scenarios:
1. **First scenario:**
- Angle at first intersection: 75 degrees (upper left).
- Angle at second intersection: 80 degrees (upper left).
- These angles are not equal, and they do not form a supplementary pair. Therefore, this scenario does not show parallel lines.
2. **Second scenario:**
- Angle at first intersection: 85 degrees (bottom left).
- Angle at second intersection: 81 degrees (upper right).
- These angles are not equal, and if they were on the same side of the transversal, they would need to add up to 180 degrees, which they do not. Therefore, this scenario does not show parallel lines.
3. **Third scenario:**
- Angle at first intersection: 130 degrees (bottom right).
- Angle at second intersection: 50 degrees (upper right).
- The angles are on the same side of the transversal. They add up to 130 + 50 = 180 degrees, which means these lines could be parallel since the same-side interior angles are supplementary.
Based on the analysis, the **third scenario** shows lines that may be parallel due to the angles being supplementary. Therefore, the diagram with the first angle at 130 degrees and the second angle at 50 degrees is the one that shows parallel lines cut by a transversal.
1. Corresponding angles are equal.
2. Alternate interior angles are equal.
3. Same-side interior angles are supplementary (sum to 180 degrees).
Now, let's analyze each set of angles given in your scenarios:
1. **First scenario:**
- Angle at first intersection: 75 degrees (upper left).
- Angle at second intersection: 80 degrees (upper left).
- These angles are not equal, and they do not form a supplementary pair. Therefore, this scenario does not show parallel lines.
2. **Second scenario:**
- Angle at first intersection: 85 degrees (bottom left).
- Angle at second intersection: 81 degrees (upper right).
- These angles are not equal, and if they were on the same side of the transversal, they would need to add up to 180 degrees, which they do not. Therefore, this scenario does not show parallel lines.
3. **Third scenario:**
- Angle at first intersection: 130 degrees (bottom right).
- Angle at second intersection: 50 degrees (upper right).
- The angles are on the same side of the transversal. They add up to 130 + 50 = 180 degrees, which means these lines could be parallel since the same-side interior angles are supplementary.
Based on the analysis, the **third scenario** shows lines that may be parallel due to the angles being supplementary. Therefore, the diagram with the first angle at 130 degrees and the second angle at 50 degrees is the one that shows parallel lines cut by a transversal.
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