Question

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

Answer 1

Well, what kind of angles are 3 and 6?

Answer 2

obtuse

Answer 3

Yes, but theres another way you can classify them based on your picture.

Answer 4

are they corresponding ?

Answer 5

alternate interior
angles

Answer 6

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 :)

Answer 7

thank you so much

Answer 8

No problem