The diagram below shows the construction EY↔ through point P parallel to NF↔

The diagram below shows the construction EY^↔ through point P parallel to NF^↔.

Which theorem justifies this method of construction?

A. If two lines in a plane are cut by a transversal to form congruent corresponding angles, then the lines are parallel.

B. If two lines in a plane are cut by a transversal to form congruent alternate exterior angles, then the lines are parallel.

C. If two lines in a plane are perpendicular to a transversal at different points, then the lines are parallel.

D. If two lines in a plane are cut by a transversal to form congruent alternative, interior angles, then the lines are parallel.

Use the figure to drag in the missing statement or reason to complete the proof.

Given: x || y and Ð6 @ Ð11.

Prove: i || m

   x                               y

     6                                  8                       l

9                                 11                           m

• Ð11 @ Ð8
• Ð6 @ Ð8
• Alternate Interior Angles Theorem
• Corresponding Angles Postulate
• Reflexive Property of Equality
• Transitive Property of Equality

1    x   2                                         3         4            l

      13       14                                       15       16         m

Tell which lines, if any are parallel based on each of the following facts. (Note: name the lines in alphabetical order!) Then state which theorem or post justifies your answer.

Ð4 @ Ð13 ?  || ?   by the ?

mÐ10 + mÐ11 = 180° makes ? || ?  by the ?

Ð9 @ Ð16 makes ? || ? by the ?

Ð7 @ Ð12 makes ? || ? by the ?

mÐ1 + mÐ3 = 180° makes ? || ? by the ?

Ð6 @ Ð14 makes ? || ? by the ?