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

Question

Mathematics

Whitney Vincent

20 May, 10:57

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

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Edward Meza · Answer 1

The transitive property states that if a ≡ b and b ≡ c, then a ≡ c.

Thus, from line 2 of the proof it is given that ∠2 ≅ ∠3 and from line 3 of the proof it is given that ∠2 ≅ ∠6, we can conclude by transitive property that ∠3 ≅ ∠6.

Therefore, the missing reason in the proof is the "transitive property".