Question

2.) given: p||q prove: ∠2≅∠8 statements reasons 1.) p||q 2.) m∠2 = m∠6 3.) m∠6 = m∠8 4.) m∠2 = m∠8 5.) ∠2≅∠8

Explanation:

Step1: Given parallel lines

Given \(p\parallel q\) (Given)

Step2: Corresponding - angles are equal

Since \(p\parallel q\), \(\angle2\) and \(\angle6\) are corresponding angles, so \(m\angle2 = m\angle6\) (Corresponding - angles postulate)

Step3: Vertical - angles are equal

\(\angle6\) and \(\angle8\) are vertical angles, so \(m\angle6 = m\angle8\) (Vertical - angles theorem)

Step4: Transitive property of equality

By the transitive property of equality, since \(m\angle2 = m\angle6\) and \(m\angle6 = m\angle8\), then \(m\angle2 = m\angle8\)

Step5: Definition of congruent angles

If \(m\angle2 = m\angle8\), then \(\angle2\cong\angle8\) (Definition of congruent angles)

Answer:

1. Given
2. Corresponding - angles postulate
3. Vertical - angles theorem
4. Transitive property of equality
5. Definition of congruent angles