Question

Given ∠3 = ∠13 , which lines, if any, must be parallel based on the given information? Justify your conclusion.


A. c || d, Converse of the Same-Side Interior Angles Theorem

B. a || b, Converse of the Alternate Interior Angles Theorem

C. not enough information to make a conclusion

D. c || d, Converse of the Corresponding Angles Theorem

Answer 1

the  correct answer  is b

Answer 2

Answer:

B.$a\parallel b$, Converse of the alternate interior angles theorem

Step-by-step explanation:

We are given that

$\angle 3=\angle 13$

We have to find the lines must be parallel based on given information .

To find the parallel lines we will use converse of alternate interior angles theorem.

Converse of alternate interior angles theorem: When alternate interior angles are equal then the  lines are parallel.

$\angle 3=\angle 13$

Reason: Given

Angle 3 and angle 13 are alternate interior angles

Therefore, by using converse of alternate interior angles theorem

Line a and b are parallel.

Hence, option B is true.