High School

We appreciate your visit to Which of the following correctly justifies statement 4 of the two column proof Lines jk and lm are intersected by transversal jl The intersection of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Which of the following correctly justifies statement 4 of the two-column proof?

Lines jk and lm are intersected by transversal jl. The intersection of jk and jl creates angles 2, 4, 3, and 1 clockwise beginning at the top right. The intersection of lm and jl creates angles 6, 8, 7, and 5 clockwise beginning at the top right.

**Given:** Line jk is parallel to line lm
**Prove:** \(\angle 3 \cong \angle 6\)

**Statement** | **Justification**
--- | ---
1. Line jk is parallel to line lm | Given
2. \(\angle 7 \cong \angle 6\) |
3. \(\angle 3 \cong \angle 7\) |
4. \(\angle 3 \cong \angle 6\) | a) Corresponding angles theorem
b) Vertical angles theorem
c) Substitution property of equality
d) Transitive property of equality

Answer :

Final answer:

The correct justification for Statement 4 (∠3 ≅ ∠6) is the transitive property of equality, following from the earlier proven statements that ∠7 ≅ ∠6 and ∠3 ≅ ∠7.

Explanation:

The correct justification for statement 4 (∠3 ≅ ∠6) in the two-column proof provided in the question is the transitive property of equality. This property states that if a = b and b = c, then a = c. In the context of this proof:

  • Statement 2 declared angles 7 and 6 to be congruent (∠7 ≅ ∠6)
  • Statement 3 declared angles 3 and 7 to be congruent (∠3 ≅ ∠7)

Following the transitive property, if ∠7 ≅ ∠6 and ∠3 ≅ ∠7, then it logically follows that ∠3 is congruent to ∠6, hence ∠3 ≅ ∠6 (Statement 4)

Learn more about the Transitive Property of Equality here:

https://brainly.com/question/14610263

#SPJ2

Thanks for taking the time to read Which of the following correctly justifies statement 4 of the two column proof Lines jk and lm are intersected by transversal jl The intersection of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Final answer:

The justification for statement 4 in the proof, claiming that ∠3 and ∠6 are congruent, is the Transitive property of equality. This is because it follows the premises that ∠7 is congruent to ∠6 and ∠3 is congruent to ∠7.

Explanation:

The justification for statement 4, ∠3 ≅ ∠6, of the two-column proof would be (d) the Transitive property of equality. Let's understand why. Initially, we have the Given that line jk is parallel to line lm. The second step establishes that ∠7 ≅ ∠6, usually through the Corresponding Angles Postulate (or Theorem), which states that when a transversal intersects parallel lines, corresponding angles are congruent. The third step establishes ∠3 ≅ ∠7, and hence by the transitive property of equality, which holds that if ∠7 ≅ ∠6 (from statement 2) and ∠3 ≅ ∠7 (from statement 3), we can deduce that ∠3 ≅ ∠6. Hence, this proof is validated.

Learn more about Two-Column Proofs here:

https://brainly.com/question/37541856

#SPJ1