Proving Lines Parallel Answers

Which theorem correctly justifies why the lines m and n are parallel when cut by transversal k?

Which diagram shows parallel lines cut by a transversal?

Letters x, y, and z are angle measures. Which equations would guarantee that lines p and q are parallel? Check all that apply.

Which lines are parallel? Justify your answer.

If angle 1 is 110°, what would the other angle measures have to be in order for m || n and q || p? Angle 2 = ⇒ 110° Angle 3 = ° Angle 4 = ⇒ 70°

Find the values of x and y that make k || j and m || n. x = ° y = °

Complete the missing parts of the paragraph proof. We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because . We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the .

angle 1 ✔ angle 2 line m

angle 1 angle 2 ✔ angle 3

corresponding angles theorem ✔ converse alternate exterior angles theorem converse same side interior angles theorem