Question

(01.07 mc)
examine the two - column proof.

given: line jk is parallel to line lm
prove: \\( \angle 1 \cong \angle 8 \\)

which of the following correctly justifies statement 4 of the two - column proof?
o a transitive property of equality
b corresponding angles theorem
c vertical angles theorem
d substitution property of equality

Explanation:

Step1: Recall properties of equality

The Transitive Property of Equality states that if \(a = b\) and \(b = c\), then \(a = c\). In this proof, we have \(\angle1\cong\angle4\) (Statement 2) and \(\angle4\cong\angle8\) (Statement 3).

Step2: Apply the property

Since \(\angle1\) is congruent to \(\angle4\) and \(\angle4\) is congruent to \(\angle8\), by the Transitive Property of Equality, \(\angle1\cong\angle8\) (Statement 4).

Answer:

A. Transitive Property of Equality