Question

Given: x ∥ y and w is a transversal
Prove: ∠3 ≅ ∠6

Parallel lines x and y are cut by transversal w. On line x where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line y where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5.

What is the missing reason in the proof?


Statement

Reason
1. x ∥ y
w is a transversal 1. given
2. ∠2 ≅ ∠3 2. def. of vert. ∠s
3. ∠2 ≅ ∠6 3. def. of corr. ∠s
4. ∠3 ≅ ∠6 4.
transitive property
symmetric property
vertical angles are congruent
definition of supplementary angles

Answer 1

Reason 4: transitive property.

Explanation: From (2) ∠2 ≅ ∠3 and (3) ∠2 ≅ ∠6, by the transitive property of congruence, ∠3 ≅ ∠6.