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

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

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.