Question

Given ∠9≅∠13.

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



Responses

c∥d, Converse of the Same-Side Interior Angles Theorem
c is parallel to d , 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

c∥d, Converse of the Corresponding Angles Theorem
c is parallel to d , 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

c ∥ d, by the Converse of the Corresponding Angles Theorem.

Reason: ∠9 and ∠13 are the lower-right angles at the intersections of transversal a with lines c and d, so they are corresponding angles. Since corresponding angles are congruent only when the two lines are parallel, c is parallel to d.