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

Answer:

A.

Step-by-step explanation:

Answer 2

Answer:

The missing reason in the proof is transitive property

Step-by-step explanation:

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.  ??????????

From the statements 2 and 3

The previous proved statement to make use of the transitive property reason or proof

∴ 4. ∠3 ≅ ∠6                                    4. transitive property

Note: the transitive property states that: If a = b and b = c, then a = c.