## BIGDOG96 3 years ago Jazz draws a transversal, t, on two parallel lines AB and CD, as shown below. He makes the following table to prove that the alternate interior angles are equal.

1. BIGDOG96

2. BIGDOG96

Statement Justification angle 2 = angle 6 Corresponding angles of parallel lines are congruent. angle 2 = angle 4 ? angle 4 = angle 6 transitive property of equality, angle 2 = angle 6, angle 2 = angle 4, therefore angle 4 = angle 6

3. BIGDOG96

4. BIGDOG96

Angles 1 and 3 are supplementary; therefore, angle 2 is equal to angle 4. Angles 1 and 3 are congruent; therefore, angle 2 is equal to angle 4. Angles 1 and 4 and angles 1 and 2 are supplementary; therefore, angle 2 is equal to angle 4. Angles 1 and 4 and angles 1 and 2 are congruent; therefore, angle 2 is equal to angle 4.

5. campbell_st

Angle 2 = Angle 4 as they are vertically opposite angles.... (sometimes called vertical angles) opposite sides of the vertex are congruent. Angle 4 = Angle 6 interior alternate angles in parallel lines are congruent. thats about the all there is...

6. BIGDOG96

So the answer is? Don't mean to be hard but you kinda confused me.

7. campbell_st

well you have proven Angle 2 = angle 4 and angle 4 = angle 6 therefore angle 2 has to equal angle 6.

8. BIGDOG96

Oh okay...but that's not a choice.

9. psi9epsilon

2=4, 6=8,1=3,5=7 are all Opp. angle which are congruent also 4 = 6 BECAUSE of two parallel lines and a kind a Z formation hint look for z formations always in a transveral, it will give you lots of information

10. BIGDOG96

Sorry but I'm still confused. I'm really sorry.

11. psi9epsilon

kindly justify?

12. BIGDOG96

I don't understand how to get the right answer.

13. BIGDOG96

Or what to do.

14. psi9epsilon

do you agree 2=4 and 4=6?

15. BIGDOG96

Yes

16. psi9epsilon

so can we say 2=6?

17. BIGDOG96

Right

18. psi9epsilon

and what kind of angles are 2 and 6 ?

19. BIGDOG96

Congruent?

20. psi9epsilon

exactly

21. psi9epsilon

we proved that they are congruent now take a careful look start from left i.e. from point A, come down and move toward ray D , does that look like a Z

22. psi9epsilon

23. BIGDOG96

Yes

24. psi9epsilon

does that help?

25. BIGDOG96

To be honest it lost me.

26. BIGDOG96

Wait is it the second choice?

27. psi9epsilon

read the reasoning above , and you have the basic information to solve the question,

28. BIGDOG96

Wait is it the second choice?

29. psi9epsilon

1 and 3, there for 2 and 4, is the closest match, 1 and 3 form a vertically oppo angle pair

30. BIGDOG96

Thanks I would give you a medal but IDK how, I new.

31. BIGDOG96

Do you have time to help me with another one?

32. psi9epsilon

sure

33. BIGDOG96

Okay

34. -GeoIzHard-

@BIGDOG96 so what was the answer.........

35. -GeoIzHard-

Was it Angles 1 and 3 are congruent; therefore, angle 2 is equal to angle 4?

36. -GeoIzHard-

@psi9epsilon @BIGDOG96