9514 1404 393
Answer:
use the transitive property and the congruence of vertical angles
Step-by-step explanation:
First of all, look at the figure and the given information, and see how that relates to the question being asked.
Here, you're given several angles between the lines of interest, all of which are congruent, and you're asked to show the lines are parallel. Two of the given angles (1 and 4) are "alternate interior angles", so the theorem relating those to parallel lines is useful.
Statement . . . . Reason
1. ∠1 ≅ ∠2, ∠3 ≅ ∠4 . . . . 1. Given
2. ∠2 ≅ ∠3 . . . . 2. Vertical angles are congruent
3. ∠1 ≅ ∠3 . . . . 3. transitive property of congruence*
4. ∠1 ≅ ∠4 . . . . 4. transitive property of congruence
5. k ║ l . . . . 5. Converse of alternate interior angles theorem**
_____
* The transitive property tells you if a ≅ b and b ≅ c, then a ≅ c.
** The alternate interior angles theorem says the alternate interior angles at a transversal crossing parallel lines are congruent. The converse says if those angles are congruent, then the lines are parallel.
