Question
Line v is parallel to line w.
Parallel lines v and w are crossed by lines s and t to form 2 triangles. At parallel line v, the angle formed by line t is 1 and formed by line s is 2. At parallel line w, the angle formed b line is 4 and line t is 5. Angles 3 and 6 are formed by s and t.
Which set of statements about the angles is true?
Angle 1 is congruent to angle 6, angle 2 is congruent to angle 4, angle 3 is congruent to angle 5
Angle 1 is congruent to angle 5, angle 2 is congruent to angle 4, angle 3 is congruent to angle 6
Angle 6 is congruent to angle 2, angle 5 is congruent to angle 4, angle 1 is congruent to angle 3
Angle 6 is congruent to angle 1, angle 3 is congruent to angle 2, angle 4 is congruent to angle 5
Parallel lines v and w are crossed by lines s and t to form 2 triangles. At parallel line v, the angle formed by line t is 1 and formed by line s is 2. At parallel line w, the angle formed b line is 4 and line t is 5. Angles 3 and 6 are formed by s and t.
Which set of statements about the angles is true?
Angle 1 is congruent to angle 6, angle 2 is congruent to angle 4, angle 3 is congruent to angle 5
Angle 1 is congruent to angle 5, angle 2 is congruent to angle 4, angle 3 is congruent to angle 6
Angle 6 is congruent to angle 2, angle 5 is congruent to angle 4, angle 1 is congruent to angle 3
Angle 6 is congruent to angle 1, angle 3 is congruent to angle 2, angle 4 is congruent to angle 5
Answers
GPT-4o mini
To analyze the relationships between the angles formed by the intersecting lines s and t with the parallel lines v and w, we can apply the concepts of corresponding angles, alternate interior angles, and consecutive interior angles.
1. **Angle 1 and Angle 6:** Since lines v and w are parallel, and line t crosses these lines, angle 1 (formed by line t at line v) and angle 6 (formed by line t at line w) are corresponding angles. Thus, angle 1 is congruent to angle 6.
2. **Angle 2 and Angle 4:** By the same reasoning, since line s also crosses the parallel lines v and w, angle 2 (formed by line s at line v) and angle 4 (formed by line s at line w) are also corresponding angles. Hence, angle 2 is congruent to angle 4.
3. **Angle 3 and Angle 5:** Angle 3 is formed by line s and line t at line w, which means that angle 3 and angle 5 are alternate interior angles. Thus, angle 3 is congruent to angle 5.
Thus, the true set of statements is:
**Angle 1 is congruent to angle 6, angle 2 is congruent to angle 4, angle 3 is congruent to angle 5.**
1. **Angle 1 and Angle 6:** Since lines v and w are parallel, and line t crosses these lines, angle 1 (formed by line t at line v) and angle 6 (formed by line t at line w) are corresponding angles. Thus, angle 1 is congruent to angle 6.
2. **Angle 2 and Angle 4:** By the same reasoning, since line s also crosses the parallel lines v and w, angle 2 (formed by line s at line v) and angle 4 (formed by line s at line w) are also corresponding angles. Hence, angle 2 is congruent to angle 4.
3. **Angle 3 and Angle 5:** Angle 3 is formed by line s and line t at line w, which means that angle 3 and angle 5 are alternate interior angles. Thus, angle 3 is congruent to angle 5.
Thus, the true set of statements is:
**Angle 1 is congruent to angle 6, angle 2 is congruent to angle 4, angle 3 is congruent to angle 5.**