Proving Lines Parallel

Parallel lines e and f are cut by transversal b. What is the value of x? 1 5 25 37

25

Lines a and b are parallel and lines e and f are parallel. What is the value of x? 8 82 98 172

82

Lines a and b are parallel and lines e and f are parallel. If m1 = 89°, what is m5? 1 89 91 179

91

Which lines are parallel? Justify your answer. Lines a and b are parallel because their corresponding angles are congruent. Lines a and b are parallel because their same side exterior angles are congruent. Lines e and f are parallel because their corresponding angles are congruent. Lines e and f are parallel because their same side exterior angles are supplementary.

Lines a and b are parallel because their corresponding angles are congruent.

Which lines are parallel? Justify your answer. Lines a and b are parallel because their alternate exterior angles are congruent. Lines a and b are parallel because their same side exterior angles are supplementary. Lines e and f are parallel because their alternate exterior angles are congruent. Lines e and f are parallel because their same side exterior angles are congruent.

Lines e and f are parallel because their alternate exterior angles are congruent.

Given the information in the diagram, which theorem best justifies why lines j and k must be parallel? alternate interior angles theorem alternate exterior angles theorem converse alternate interior angles theorem converse alternate exterior angles theorem

converse alternate exterior angles theorem

Letters a, b, c, and d are angle measures. Which should equal 105° to prove that f ∥ g? a b c d

d

Given: and Prove: m∠1 = m∠4 m∠2 = m∠3 m∠1 + m∠4 = 180° m∠2 + m∠3 = 180°

m∠1 + m∠4 = 180°

Letters w, x, y, and z are angle measures. Which should equal 92° to prove that r ∥ s? w x y z

w

Lines c and d are parallel lines cut by transversal p. Which must be true by the corresponding angles theorem? ∠1 ≅ ∠7 ∠2 ≅ ∠6 ∠3 ≅ ∠5 ∠5 ≅ ∠7

∠2 ≅ ∠6