Homework: pg. 166 #s 12-29
12. Angle 3 is congruent to angle 7 by corresponding angles. Line l is parallel to line m by the Converse of
the corresponding angles postulate.
13. Measure of angle 8 is (7(7) + 5) = 54. Measure of angle 4 is 54. By transitive property, measure of
angle 8 is equal to measure of angle 4. They are congruent because they are corresponding angles. Line l
is parallel to line m by the Converse of the corresponding angles postulate.
14. Measure of angle 2 is (8(15) + 4) = 124. Measure of angle 6 is (11(15) -41) = 124. Measure of angle 2
equals measure of angle 6 by the transitive property. They are congruent because they are
corresponding angles. Line l is parallel to line m by the Converse of the corresponding angles postulate.
15. Measure of angle 1 is (3(12) + 19) = 55. Measure of angle 5 is (4(12)+7) = 55. Angle 1 is congruent to
Angle 5 by corresponding angles. Line l is parallel to line m by the Converse of the corresponding angles
postulate.
16. Angle 3 and angle 6 are alternate interior angles. Line n is parallel to line p by the converse of
alternate interior angles theorem.
17. Angle 2 and angle 7 are alternate exterior angles. Line n is parallel to line p by the converse of
alternate exterior angles theorem.
18. Angle 4 and angle 6 are same-side interior angles. Line n is parallel to line p by the converse of sameside interior angles theorem.
19. Measure of angle 1 = 105. Measure of angle 8 = 105. They are congruent because they are alternate
exterior angles. Line n is parallel to line p by the converse of alternate exterior angles theorem.
20. Measure of angle 4 = 103. Measure of angle 5 = 103. They are congruent because they are alternate
interior angles. Line n is parallel to line p by the converse of alternate interior angles theorem.
21. Measure of angle 3 = 75. Measure of angle 5 = 105. 75 + 105 = 180. Therefore Measure of angle 3 +
measure of angle 5 = 180 because they are same-side interior angles. Line n is parallel to line p by the
converse of same-side interior angles theorem.
22.
a. Corresponding angles postulate
b. Given
c. Transitive Property of Congruence
d. BC is parallel to DE
e. Converse of Corresponding Angles Postulate
23. Measure of angle 1 = 20 and measure of angle 2 = 20. Both angles are corresponding angles.
Therefore, DJ is parallel to EK by converse of corresponding angles postulate.
24. Converse of Corresponding Angles Postulate
25. Converse of Alternate exterior angles theorem
26. converse of alternate interior angles theorem
27. converse of corresponding angles postulate
28. converse of alternate interior angles theorem
29. converse of same-side interior angles theorem