Question

we see that ∠1 and ∠2 are choose one
thus, ∠1 and ∠2 are choose one
so, m∠2 =
we see that ∠2 and ∠3 are choose one
and since the lines s and t are parallel, ∠2 and ∠3 are choose one
so, m∠3 =
therefore, ∠1 and ∠3 are choose one
we also see that ∠1 and ∠3 are choose one
the relationship between ∠1 and ∠3 is an example of the following rule.
when parallel lines are cut by a transversal, choose one

complete the statements below.
the relationship between ∠1 and ∠3 is an example of the following rule.
when parallel lines are cut by a transversal, choose one

Explanation:

1. Explanation:

• First, we identify the angle - pair relationships.
• Step1: Relationship between ∠1 and ∠2
• ∠1 and ∠2 are vertical angles. Vertical angles are congruent. So, \(m\angle1 = m\angle2\).
• Step2: Relationship between ∠2 and ∠3
• Since lines \(s\) and \(t\) are parallel and \(w\) is a transversal, ∠2 and ∠3 are corresponding angles. Corresponding angles formed by parallel lines cut by a transversal are congruent. So, \(m\angle2=m\angle3\).
• Step3: Relationship between ∠1 and ∠3
• Because \(m\angle1 = m\angle2\) and \(m\angle2=m\angle3\), by the transitive property of equality, \(m\angle1=m\angle3\). Also, ∠1 and ∠3 are alternate - exterior angles. When parallel lines are cut by a transversal, alternate - exterior angles are congruent.

1. Answer:

• We see that ∠1 and ∠2 are vertical angles. Thus, ∠1 and ∠2 are congruent. So, \(m\angle2 = m\angle1\).
• We see that ∠2 and ∠3 are corresponding angles. And since the lines \(s\) and \(t\) are parallel, ∠2 and ∠3 are congruent. So, \(m\angle3 = m\angle2\).
• Therefore, ∠1 and ∠3 are alternate - exterior angles. We also see that ∠1 and ∠3 are congruent.
• The relationship between ∠1 and ∠3 is an example of the following rule: When parallel lines are cut by a transversal, alternate - exterior angles are congruent.

Answer:

1. Explanation:

• First, we identify the angle - pair relationships.
• Step1: Relationship between ∠1 and ∠2
• ∠1 and ∠2 are vertical angles. Vertical angles are congruent. So, \(m\angle1 = m\angle2\).
• Step2: Relationship between ∠2 and ∠3
• Since lines \(s\) and \(t\) are parallel and \(w\) is a transversal, ∠2 and ∠3 are corresponding angles. Corresponding angles formed by parallel lines cut by a transversal are congruent. So, \(m\angle2=m\angle3\).
• Step3: Relationship between ∠1 and ∠3
• Because \(m\angle1 = m\angle2\) and \(m\angle2=m\angle3\), by the transitive property of equality, \(m\angle1=m\angle3\). Also, ∠1 and ∠3 are alternate - exterior angles. When parallel lines are cut by a transversal, alternate - exterior angles are congruent.

1. Answer:

• We see that ∠1 and ∠2 are vertical angles. Thus, ∠1 and ∠2 are congruent. So, \(m\angle2 = m\angle1\).
• We see that ∠2 and ∠3 are corresponding angles. And since the lines \(s\) and \(t\) are parallel, ∠2 and ∠3 are congruent. So, \(m\angle3 = m\angle2\).
• Therefore, ∠1 and ∠3 are alternate - exterior angles. We also see that ∠1 and ∠3 are congruent.
• The relationship between ∠1 and ∠3 is an example of the following rule: When parallel lines are cut by a transversal, alternate - exterior angles are congruent.