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.
a. m∠1 = m∠4
b. m∠2 = m∠3
c. m∠1 + m∠4 = 180°
d. m∠2 + m∠3 = 180°