What is the reason for the third step in this proof? Given: a || b, and both lines are cut by transversal t. Prove: 2 7 Proof: Statement Reason 1. a || b given 2. 2 3 Vertical Angles Theorem 3. 3 6 4. 2 6 Transitive Property of Congruence 5. 6 7 Vertical Angles Theorem 6. 2 7 Transitive Property of Congruence Transitive Property of Equality Alternate Interior Angles Theorem Corresponding Angles Theorem Same-Side Interior Angles Theorem Vertical Angles Theorem

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What is the reason for the third step in this proof? Given: a || b, and both lines are cut by transversal t. Prove: 2 7 Proof: Statement Reason 1. a || b given 2. 2 3 Vertical Angles Theorem 3. 3 6 4. 2 6 Transitive Property of Congruence 5. 6 7 Vertical Angles Theorem 6. 2 7 Transitive Property of Congruence Transitive Property of Equality Alternate Interior Angles Theorem Corresponding Angles Theorem Same-Side Interior Angles Theorem Vertical Angles Theorem

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Well, what kind of angles are 3 and 6?
obtuse

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Yes, but theres another way you can classify them based on your picture.
are they corresponding ?
alternate interior angles
Ah, okay. Well, you'll have to learn how to classify the angles. Like, if we just ignored what the question was asking, we would have to know what all the angles are relative to each other. Like step 2 said, angles 2 and 3 are vertical angles. 1 and 4 are also vertical angles, as well as 5 and 8, 6 and 7. But yes, they are alternate interior angles, so thats the theorem thats needed here :) 4 and 5 are also alternate interior angles. This problem doesnt need that, but you should be able to get that. So yeah, try and get used to being able to classify angles. Should be able to name pairs of alternate exterior, adjacent, corresponding, etc. But yes, 3 and 6 are alternate interior angles, so thats the step in the proof :)
thank you so much
No problem

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