Proving Lines Parallel

Parallel lines e and f are cut by transversal b. What is the value of y? 16 50 130 164

130

What must be the value of x so that lines a and b are parallel lines cut by transversal f? 10 20 22 32

22

In the diagram, g ∥ h, m∠1 = (4x + 36)°, andm∠2 = (3x - 3)°. What is the measure of ∠3? 21° 60° 120° 159°

60

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 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

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°

Which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f? m∠4 = 110° and m∠3 = 70° m∠1 = 110° and m∠2 = 110° m∠1 = 110° and m∠3 = 70° m∠2 = 110° and m∠3 = 110°

m∠1 = 110° and m∠3 = 70°

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