Which lines, if any, must be parallel based on the given information? Justify your conclusion.

Given: ∠3 is congruent to ∠13

- c || d, Converse of the Corresponding Angles Postulate

- a || b, Converse of the Alternate Interior Angles Theorem

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

- Not enough information to make a conclusion

a must be parallel to b.

Proof:
∠3 = ∠13 (given)
∠15 = ∠13 (vertically opposite angles are equal)
Since ∠13 = ∠3 and ∠13 = ∠15, ∠15 = ∠3

Then, a must be parallel to b (transverse line d cuts parallel lines producing converse alternate angles that are equal (ie ∠15 = ∠3))

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akposevictor akposevictor · Answer 2 · 2021-10-29T11:17:15+02:00

Since we know that, [tex]\angle 3 \cong \angle 13[/tex], we can conclude based on the information given that: B. a || b based on the Converse of the Alternate Interior Angles Theorem

Recall:

Two angles that lie on opposite sides of a transversal but are positioned inside the parallel lines the transversal cut across are congruent by the alternate interior angles theorem.
Conversely, for if alternate interior angles are congruent, the lines they are found on are parallel to each other.

Thus,

we are given that [tex]\angle 3 \cong \angle 13[/tex], and they are found on lines a and b.

Therefore, since we know that, [tex]\angle 3 \cong \angle 13[/tex], we can conclude based on the information given that: B. a || b based on the Converse of the Alternate Interior Angles Theorem

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