Question

Determine the theorem that justifies each if-then statement

a. If line p is parallel to liner, then 22 a 27.
b. If line p is parallel to liner, then 24 = 25.
c. If 2326, the line p is parallel to liner.
d. If line p is parallel to liner, then 21 = 25.
e. If line p is parallel to liner, then m24+ m26 = 180°
f. If line p is parallel to liner, then m2 + m27 = 180'

Answer 1

The theorem that justifies each of the given if-then statements is the Parallel Lines and Transversals Theorem. According to this theorem, if two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Step-by-step explanation:

The theorem that justifies each of the given if-then statements is the Parallel Lines and Transversals Theorem. According to this theorem, if two parallel lines are cut by a transversal, then the corresponding angles are congruent. In the given statements:

1. If line p is parallel to line r, then angle 22 is congruent to angle 27.
2. If line p is parallel to line r, then angle 24 is congruent to angle 25.
3. If angle 23 is congruent to angle 26, then line p is parallel to line r.
4. If line p is parallel to line r, then angle 21 is congruent to angle 25.
5. If line p is parallel to line r, then the sum of angle 24 and angle 26 is 180 degrees.
6. If line p is parallel to line r, then the sum of angle 2 and angle 27 is 180 degrees.