1. 5.3 By: Jennie Page and Grace Arnold

2.  Apply the Parallel Postulate  Identify the pairs of angles formed by a transversal cutting parallel lines  Apply six theorems about parallel lines

3.  Through a point not on a line there is exactly one parallel to the given line A

4.  If two parallel lines are cut by a transversal each pair of alternate interior angles are congruent.  (short form:||lines alt. int.  s ) a b

5.  If two parallel lines are cut by a transversal, then any pairs of angles formed are either congruent or supplementary. x x (180-x) x x a b

6.  If two parallel lines are cut by a transversal, each pair of alternate exterior angles are congruent.  (short form:||lines alt. ext.  s ) a b

7.  If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent.  (short form: || lines corr.  s ) a b

8.  If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary.  (short form: || lines same sided int.  s supp.) a b

9.  If two parallel lines are cut by a transversal, each pair of exterior angles on the same side of the transversal are supplementary.  (short form: || lines same sided ext.  s supp.) a b

10.  In a plane, if a line is perpendicular to one of two parallel lines, it is perpendicular to the other. a b c

11.  If two lines are parallel to a third line, they are parallel to each other. (Transitive Property of Parallel Lines) abcabc If a || b and a || c then, b || c

12. 1202 34 5 6 78 From the given angle that is 120, name the degrees of the other angles. 1 st sample problem

13. 120  2 = 60  3= 60  4=120  5 =120  6=60  7=60  8=120  1 =  1  4,  2  3,  5  8,  6  7 because vertical angles are congruent.  1  8,  2  7 because alternate exterior angles are congruent.  3  6,  5  4 because alternate interior angles are congruent.  1  5,  2  6,  3  7,  4  8 because corresponding angles are congruent.  3 supp.  5,  4 supp.  6 because same sided int. angles are supp.  1 supp.  7,  2 supp.  8 because same sided ext. angles are supp.

14.  Use the given information to name the segments that must be ||. If there are no such segments, say so. ABCDEFABCDEF

15.  A. PL || AR  B. PA || LR  C. None  D. PL || AR  E. None

16. This is an example of a crook problem. 180-34=146 (alt int. angles are congruent) Half of the x is 34 Once again because alt. int. angles are congruent the bottom half of the x is 28. Therefore, x= 28+34=62

17. What is the value of x?

18. Given: K||P Prove:  1  3

19.  1. 25 Alternate int. angles are congruent 2x-10=65-x 3x=75 x=25  2. 20 Corr. Angles are congruent x+80=5x 80=4x x=20  3. 33 3x+15+ 2x= 180 5x+15= 180 5x= 165 x= 33

20.  Statements 1. k||p 2.  1  2 3.  2  3 4.  1  3 Reasons 1. Given 2. || lines corr.  s 3. Vertical angles are 4. Transitive