Question

8
complete the following proof using theorems, definitions, and/or properties to prove the correspon angles theorem.
given: k || l
prove: ∠2≅∠4
statements reasons

1. k || l 1. given
2. ∠8≅∠4 2.
3. ∠2≅∠8 3.
4. ∠2≅∠4 4.

Explanation:

Step1: Identify corresponding - angles

Since \(k\parallel l\), \(\angle8\) and \(\angle4\) are corresponding angles. By the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then corresponding angles are congruent. So, \(\angle8\cong\angle4\).

Step2: Identify vertical - angles

\(\angle2\) and \(\angle8\) are vertical angles. By the Vertical Angles Theorem, vertical angles are congruent. So, \(\angle2\cong\angle8\).

Step3: Use transitive property

The transitive property of congruence states that if \(a\cong b\) and \(b\cong c\), then \(a\cong c\). Since \(\angle2\cong\angle8\) and \(\angle8\cong\angle4\), we can conclude that \(\angle2\cong\angle4\).

Answer:

Statements	Reasons
2. \(\angle8\cong\angle4\)	2. Corresponding Angles Postulate
3. \(\angle2\cong\angle8\)	3. Vertical Angles Theorem
4. \(\angle2\cong\angle4\)	4. Transitive Property of Congruence