Question
Which pairs of angles are corresponding angles? Select all that apply.
There are two vertical parallel lines which intersected by one line. The first vertical line and other line make angles 1 and 3 at upper side and 2 and 4 at below. The angles 1 and 4 are opposite to each other. The angles 2 and 3 are opposite to each other. The second vertical line and other line make angles 5 and 7 at upper side and 6 and 8 at below. The angles 5 and 8 are opposite to each other. The angles 6 and 7 are opposite to each other.
A. ∠1 and ∠5
B. ∠1 and ∠2
C. ∠2 and ∠8
D. ∠3 and ∠7
E. ∠4 and ∠8
There are two vertical parallel lines which intersected by one line. The first vertical line and other line make angles 1 and 3 at upper side and 2 and 4 at below. The angles 1 and 4 are opposite to each other. The angles 2 and 3 are opposite to each other. The second vertical line and other line make angles 5 and 7 at upper side and 6 and 8 at below. The angles 5 and 8 are opposite to each other. The angles 6 and 7 are opposite to each other.
A. ∠1 and ∠5
B. ∠1 and ∠2
C. ∠2 and ∠8
D. ∠3 and ∠7
E. ∠4 and ∠8
Answers
Answered by
GPT-4o mini
To determine which pairs of angles are corresponding angles, we first need to understand the definition of corresponding angles. When two parallel lines are cut by a transversal, the pairs of angles that are in the same relative position at each intersection are called corresponding angles.
Based on your description of the angles formed by two vertical parallel lines and a transversal:
1. The angles at the intersection with the first vertical line and the transversal are:
- Angle 1 (upper left)
- Angle 2 (lower left)
- Angle 3 (upper right)
- Angle 4 (lower right)
2. The angles at the intersection with the second vertical line and the transversal are:
- Angle 5 (upper left)
- Angle 6 (lower left)
- Angle 7 (upper right)
- Angle 8 (lower right)
Now, we can determine the corresponding angles:
- **∠1 and ∠5**: Both are in the upper left position at their respective intersections → Corresponding angles.
- **∠1 and ∠2**: These are on the same line, but opposite to each other → Not corresponding angles.
- **∠2 and ∠8**: ∠2 is lower left and ∠8 is lower right → Not corresponding angles.
- **∠3 and ∠7**: Both are in upper right position at their respective intersections → Corresponding angles.
- **∠4 and ∠8**: Both are in lower right position at their respective intersections → Corresponding angles.
Thus, the pairs of angles that are corresponding angles are:
- A. ∠1 and ∠5
- D. ∠3 and ∠7
- E. ∠4 and ∠8
Final answer: A, D, E.
Based on your description of the angles formed by two vertical parallel lines and a transversal:
1. The angles at the intersection with the first vertical line and the transversal are:
- Angle 1 (upper left)
- Angle 2 (lower left)
- Angle 3 (upper right)
- Angle 4 (lower right)
2. The angles at the intersection with the second vertical line and the transversal are:
- Angle 5 (upper left)
- Angle 6 (lower left)
- Angle 7 (upper right)
- Angle 8 (lower right)
Now, we can determine the corresponding angles:
- **∠1 and ∠5**: Both are in the upper left position at their respective intersections → Corresponding angles.
- **∠1 and ∠2**: These are on the same line, but opposite to each other → Not corresponding angles.
- **∠2 and ∠8**: ∠2 is lower left and ∠8 is lower right → Not corresponding angles.
- **∠3 and ∠7**: Both are in upper right position at their respective intersections → Corresponding angles.
- **∠4 and ∠8**: Both are in lower right position at their respective intersections → Corresponding angles.
Thus, the pairs of angles that are corresponding angles are:
- A. ∠1 and ∠5
- D. ∠3 and ∠7
- E. ∠4 and ∠8
Final answer: A, D, E.