Proving Lines Parallel

Letters a, b, c, and d are angles measures. Which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? Select three options. a = c a = d c = d b + c = 180° b + d = 180°

B,C and E

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

b

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

b

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

b

Which diagram shows lines that must be parallel lines cut by a transversal?

b

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

c

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

c

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

c

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.

c

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°

c

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

d