Question

Given ∠4≅∠14, which lines, if any, must be parallel based on the given information?

Justify your conclusion.



Responses

a∥b, converse of the same-side interior angles theorem
a is parallel to b , converse of the same-side interior angles theorem

a∥b, converse of the alternate interior angles theorem
a is parallel to b , converse of the alternate interior angles theorem

a∥b, converse of the corresponding angles theorem
a is parallel to b , converse of the corresponding angles theorem

not enough information to make a conclusion
not enough information to make a conclusion
Two horizontal, parallel lines, line c and line d, where line c is above line d. These lines are intersected by two diagonal parallel lines, line a and line b. Line a is to the left of line b. The angles created by each intersection are numbered. From top left, going clockwise, the angles where line a intersects line c are labeled eleven, ten, nine, and twelve. The angles where line b intersects line c are labeled seven, six, five, and eight. The angles where line a intersects line d are labeled fifteen, fourteen, thirteen and sixteen. The angles where line b intersects line d are labeled three, two, one and four.

Answer 1

a∥b, converse of the alternate interior angles theorem.

Reason: ∠14 and ∠4 are alternate interior angles formed by lines a and b with transversal d. Since those alternate interior angles are congruent, the converse of the alternate interior angles theorem implies a ∥ b.