Question

Which segments are parallel? Justify your answer.

_ are parallel by the_

A. No lines
B. NB and DH
C. RN and BD

A. Converse of the alternate exterior angles theorem
B. Converse of the corresponding angles postulate
C. Converse of the same-side interior angles theorem
D. Converse of the alternate interior angles theorem

Answer 1

B. NB and DH

B. converse of corresponding angles theorem

Explanation:

The transversal in this geometry is line BH. The angles marked 36° are on the same side of the transversal, and on the same sides of the intersecting lines NB and DH. That makes these congruent angles "corresponding" angles.

Segments NB and DH are parallel by the converse of the corresponding angles postulate.

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Additional comment

The corresponding angles postulate tells you corresponding angles are congruent where a transversal crosses parallel lines. Its converse tells you the lines are parallel if the corresponding angles are congruent.

Corresponding angles lie in the same direction from the vertex where the transversal meets one of the parallel lines. Here, the angles are "northwest" of the vertex.