Proving Lines Parallel

Lines e and f are intersected by lines a and b. At the intersection of lines a and e, the uppercase right angle is 110 degrees. At the intersection of lines b and e, the uppercase right angle is 110 degrees. At the intersection of lines b and f, the bottom right angle is 80 degrees. Which lines are parallel? Justify your answer.

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

Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are: 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s?

A: w

In the diagram, g ∥ h, m∠1 = (4x + 36)°, and m∠2 = (3x - 3)°. Lines g and h are parallel and diagonal down to the right. A horizontal line cuts through lines g and h. Another vertical line goes through lines g and h and the horizontal line. At the intersection of the vertical line with line h, the bottom left angle is angle 1 and the bottom right angle is angle 3. At the intersection of the vertical line with line g, the uppercase left angle is angle 2. What is the measure of ∠3?

B: 60°

Lines a and b are parallel and lines e and f are parallel. Horizontal lines e and f are intersected by lines a and b. At the intersection of lines a and e, the uppercase left angle is 82 degrees, and the bottom left angle is 98 degrees. At the intersection of lines b and e, the bottom right angle is x degrees. What is the value of x?

B: 82

Letters a, b, c, and d are angles measures. Lines m and n are cut by transversal p. At the intersection of lines p and m, labeled clockwise, from uppercase left, the angles are: a, b, c, blank. At the intersection of lines p and n, labeled clockwise, from uppercase left, the angles are: blank, blank, d, blank. Which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? Select three options.

B: a = d C: c = d E: b + d = 180°

Lines c and d are parallel lines cut by transversal p. Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8. Which must be true by the corresponding angles theorem?

B: ∠2 ≅ ∠6

Parallel lines e and f are cut by transversal b. Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 18) degrees. At the intersection of lines b and f, the top right angle is (4 x minus 14) degrees and the bottom right angle is y degrees. What is the value of y?

C: 130

Parallel lines e and f are cut by transversal b. Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 10) degrees. At the intersection of lines b and f, the bottom left angle is (3 x minus 15) degrees. What is the value of x?

C: 25

Lines a and b are parallel and lines e and f are parallel. Vertical and parallel lines a and b are intersected by horizontal lines e and f. At the intersection of lines a and e, the top left angle is angle 1 and the top right angle is angle 2. At the intersection of lines b and e, the bottom left angle is angle 3. At the intersection of lines b and f, the uppercase right angle is angle 4 and the bottom left angle is angle 5. If m1 = 89°, what is m5?

C: 91

Horizontal lines e and f are intersected by lines a and b. At the intersection of lines a and e, the uppercase left angle is 75 degrees. At the intersection of lines b and e, the uppercase right angle is 115 degrees. At the intersection of lines a and f, the bottom right angle is 75 degrees. Which lines are parallel? Justify your answer.

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

Given: Line segment A B is parallel to line segment D C and Measure of angle 2 equals measure of angle 4 Prove: Line segment A D is parallel to line segment B C A parallelogram has points A B C D. Angle D A B is angle 1, Angle A B C is angle 2, Angle B C D is angle 3, and angle C D A is angle 4. A 2-column table with 7 rows. Column 1 is labeled statements and has entries line segment A B is parallel to line segment D C, measure of angle 2 = measure of angle 4, angle 1 and angle 4 are supplements, question mark, measure of angle 1 + measure of angle 2 = 180 degrees, angle 1 and angle 2 are supplements, line segment A D is parallel to line segment B C. Column 2 is labeled reasons with entries given, given, same side interior angles theorem, definition of supplementary angles, substitution, definition of supplementary angles, converse same side interior angles theorem.

C: m∠1 + m∠4 = 180°

Lines j and k are intersected by line m. At the intersection of lines j and m, the uppercase left angle is 93 degrees. At the intersection of lines k and m, the bottom right angle is 93 degrees. Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?

D: converse alternate exterior angles theorem

Letters a, b, c, and d are angle measures. Lines f and g are intersected by line n. At the intersection of lines n and g, clockwise from the top, the angles are: a, 75 degrees, blank, b. At the intersection of lines n and f, clockwise from the top, the angles are blank, blank, d, c. Which should equal 105° to prove that f ∥ g?

D: d