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Answer :
Statement 4 is justified by the Vertical Angles Theorem because ∠22 and ∠27 are vertical angles formed when the lines JK and LM intersect, and vertical angles are congruent.
Option (C) is true.
We have,
The Vertical Angles Theorem states that when two lines intersect, the pairs of opposite angles (vertical angles) are congruent.
In the given two-column proof:
Statement 1 states that JK is parallel to LM, which is the given information.
Statement 2 claims that ∠26 ≅ ∠27, which means that angle ∠26 and angle ∠27 have the same measure.
Statement 3 asserts that ∠22 ≅ ∠26, indicating that angle ∠22 and angle ∠26 have the same measure.
Now, in statement 4, it is concluded that ∠22 ≅ ∠27, which means that angle ∠22 and angle ∠27 also have the same measure.
This conclusion is justified by the Vertical Angles Theorem because ∠22 and ∠27 are vertical angles formed when the lines JK and LM intersect.
Therefore, the measure of angle ∠22 is equal to the measure of angle ∠27, and this is why the justification is based on the Vertical Angles Theorem.
Hence, option (C) is true.
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The complete question:
"Which of the following correctly justifies statement 4 of the two-column proof?"
Given:
JK || LM (Given)
Prove:
2. ∠26 ≅ ∠27
∠22 ≅ ∠26
∠22 ≅ ∠27
Justification Options:
A. Corresponding Angles Theorem
B. Transitive Property of Equality
C. Vertical Angles Theorem
D. Substitution Property of Equality
Choose the correct justification for statement 4: A, B, C, or D.
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