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:

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.

Answer 2

The missing reason in the proof that makes ∠3 ≅ ∠6 is: a. transitive property.

• We are given the proof of $\angle 3 \cong \angle 6$ .

• We are required to find the missing reason that will complete the proof.

The diagram containing the sketch of the details given is in the attachment below.

Since it has been proven that:

• $\angle 2 \cong \angle 3$ - based on the stated reason that they are vertical angles which are equal to each other.

• $\angle 2 \cong \angle 3$ - based on the stated reason that they are corresponding angles

Therefore, applying the transitive property which says:

• $if x = y, and \\\\y = z, then\\\\x = z$

We can in the same vein state the following:

• $if,\\\angle 2 \cong \angle 3, and\\\\\angle 3 \cong \angle 6, then\\\\\angle 3 \cong \angle 6$

This follows the same line of thought with the transitive property illustrated earlier.

Therefore, the missing reason in the proof that makes ∠3 ≅ ∠6 is: a. transitive property.

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