Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer. Given
a. <10 congruent <15
b. m<14 + m<18 = 180°
c. <4 congruent 20
d. <3 congruent <16
e. <10 congruent <12
f. m<7 + m<19 = 180°
g. <6 congruent <17
h. <9 congruent <24
i. <2 congruent <21
j. m<3 + m<7 = 180°
k. <6 congruent <11
I. <1 congruent <3
m. <12 congruent <15
n. m<13 + m<16 = 180°
o. <15 congruent <18

Parallel Lines
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Converse
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Parallel lines

a. Line j is parallel to line k

b. Line m is parallel  to line n

c. Line l is parallel to line n

d. Line l is parallel to line m

e. Line j is parallel to line k

g. Line l is parallel to line n

h. Line m is parallel to line n, given that line j is parallel to line k

i. Line l is parallel to line n

j. Angles on a straight line

k. Line j is parallel to line k, Line l is parallel to line m

l. Line j is parallel to line k

m. Vertically opposite angles

n. Line j is parallel to line k

o. Line m is parallel to line n, and Line j is parallel to line k

Converse

a. Alternate interior angles of parallel lines are congruent

b. Consecutive interior angles of parallel lines are supplementary

c. Corresponding angles of parallel lines are congruent

d. Alternate exterior angles of parallel lines are congruent

e. Corresponding angles of parallel lines are congruent

g. Alternate interior angles of parallel lines are congruent

h. Opposite angles of a parallelogram are congruent

i. Alternate exterior angles of parallel lines are congruent

j. Angles on a straight line

k. Opposite angles of a parallelogram are congruent

l. Corresponding angles of parallel lines are congruent

m. Vertically opposite angles

n. Same side exterior angles are supplementary for two parallel lines

o. Opposite angles of a parallelogram are congruent

Step-by-step explanation:

a. Alternate interior angles of parallel lines are congruent, therefore;

Line j is parallel to line k

b. Consecutive interior angles of parallel lines are supplementary, therefore;

Line m is parallel  to line n

c. Corresponding angles of parallel lines are congruent, therefore;

Line l is parallel to line n

d. Alternate exterior angles of parallel lines are congruent, therefore;

Line l is parallel to line m

e. Corresponding angles of parallel lines are congruent, therefore;

Line j is parallel to line k

g. Alternate interior angles of parallel lines are congruent, therefore;

Line l is parallel to line n

h. Opposite angles of a parallelogram are congruent, therefore;

Line m is parallel to line n, given that line j is parallel to line k

i. Alternate exterior angles of parallel lines are congruent, therefore;

Line l is parallel to line n

j. Angles on a straight line

k. Opposite angles of a parallelogram are congruent

Line j is parallel to line k, Line l is parallel to line m

l. Corresponding angles of parallel lines are congruent, therefore;

Line j is parallel to line k

m. Vertically opposite angles

n. Same side exterior angles are supplementary for two parallel lines

Line j is parallel to line k

o. Opposite angles of a parallelogram are congruent

Line m is parallel to line n, and Line j is parallel to line k.