An information that CANNOT be used to prove that j || k include the following: D. ∠1 is supplementary to ∠2.
In Mathematics and Euclidean Geometry, parallel lines are always coplanar lines and straight lines that have an equal distance between each other. Hence, corresponding angles or vertically opposite angles are congruent in all parallel lines that are cut through by a transversal.
By applying the alternate interior angles theorem to parallel lines j and k cut through by a transversal, we have the following pair of congruent angles;
m∠7 ≅ m∠3
m∠6 ≅ m∠2
By applying consecutive interior angles theorem to parallel lines j and k, we have the following supplementary angles:
m∠7 + m∠6 = 180°.
By applying the alternate exterior angles theorem to parallel lines j and k cut through by a transversal, we have the following pair of congruent angles;
m∠1 ≅ m∠5
In conclusion, angle 1 being supplementary to angle 2 cannot be used to prove that line j is parallel to line k.
Complete Question:
Which information CANNOT be used to prove that j || k?
A. ∠7 ≅ ∠3
B ∠7 is supplementary to ∠6.
C. ∠1 ≅ ∠5
D. ∠1 is supplementary to ∠2.