If parallel lines are cut by a transversal, then: - Corresponding angles are congruent - Alternate interior angles are congruent - Alternate exterior angles are congruent - Interior angles on the same side of the transversal are supplementary - Exterior angles on the same side of the transversal are supplementary

1. PARALLEL LINE PROPERTIES

2. WORKING TOGETHERDraw two parallel lines using lined paper or the two edges of a ruler. Then draw a transversal that intersects the two parallel lines obliquely.Label all the angles from 1 to 8.List all pairs of corresponding, alternate interior, alternate exterior , same side interior and same side exterior angles.

3. WORKING TOGETHERObserve the measurements and make conjectures about the measures of the angle pairs. Write your conclusions in if-then form.Compare your results with those of your classmates.

4. If parallel lines have a transversal, then… (l ║ m)(n)Corresponding angles are congruentAlternate interior angles are congruentAlternate exterior angles are congruent1 5 2 637 4 812l3456m3 5 4 678n1 7 2 8

5. If a transversal (n) cuts two parallel lines (l ║ m), then all pairs of interior angles on the same side of the transversal are supplementary.3 + 6 = 18004 + 5 = 1800They are same-side interior angles.If a transversal (n) cuts two parallel lines (l ║ m), then all pairs of exterior angles angles on the same side of the transversal are supplementary.2 + 7 = 18001 + 8 = 1800They are same-side exterior angles.12l3456m78n

6. If a transversal is perpendicular to one of two parallel lines, then it is also perpendicular to the other. Given: l ║ m , l┴ nThus, m┴ n┌1l5mn

7. SUMMARYCorresponding angles are congruent. PCAC TheoremAlternate interior angles are congruent. PAIC * Parallel lines are indicated as lines with the same number of arrowheads located near the center.

8. Alternate exterior angles are congruent. PAEC TheoremInterior angles on the same side of a transversal are supplementary. PSSIAS TheoremExterior angles on the same side of a transversal are supplementary. PSSEAS Theorem3j 3 4h42 1 + 2 = 180013 3 + 4 = 18004

9. If a transversal obliquely intersects two parallel lines, then:All the acute angles are congruent. All the obtuse angles are congruent.Any pair of acute and obtuse angle is supplementary.

10. SUMMARYIf parallel lines are cut by a transversal, thenCorresponding angles are congruent.Alternate interior angles are congruent.Alternate exterior angles are congruent.Same side interior angles are supplementary.Same side exterior angles are supplementary.

11. Sample Problems1.2.a(5x - 10)0Same Side Interior Angles(8x + 34)0bsupplementary angles(7x + 54)0Alternate Interior Anglescongruent angles(3x + 90)0

12. Sample Problems3.4.(8x – 8)oAlternate Exterior Angles(6x + 48)ocongruent angles(5x + 20)oCorresponding Anglescongruent angles(8x + 2)o

13. SeatworkAnswer nos. 20 – 22in your E-Math book page 112in ½ paper (crosswise)

14. The importance of learning this…Take a look around you.Chances are, you can see an example of parallel lines from where you are sitting.But how can you be sure the lines you see are parallel?Architects and builders use the basic geometric concepts in this chapter to insure that lines are indeed parallel.

15. PROVINGLINES PARALLELpg 91

16. If two lines have…a transversal and a pair of congruent corresponding angles,a transversal and a pair of congruent alternate interior angles,a transversal and a pair of congruent alternate exterior angles,interior angles on the same side of the transversal that are supplementary,exterior angles on the same side of the transversal that are supplementary,then the lines are parallelIf two coplanar lines are perpendicular to the same line,

17. Examples1.2.5.YES, alternate interior angles are congruent13001300NO. The corresponding angles are not congruent. Therefore, they are not parallel.┌700YES, because the two lines are perpendicular to the same line.┌┌

18. TRANSVERSALSIN REALITY