2. Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________. 2. Vertical angles have equal measures, so they are ______________. 3. Angles whose measures have a sum of 180° are ______________. 4. A part of a line between two points is called a ____________. 5. Find the measure s of a, b, and c in the picture. complementary congruent supplementary segment a °= 140° b °= 40° c°= 140° Warm Up

3. Parallel & Perpendicular Lines A NGLE R ELATIONSHIP

4. Learn to identify parallel and perpendicular lines and the angles formed by a transversal. Parallel lines are lines in a plane that never meet, like a set of perfectly straight, infinite train tracks. Perpendicular lines are lines that intersect at 90° angles.

5. D EFINITIONS Two lines that do not intersect are either parallel or skew. Parallel lines do not intersect and are coplanar Skew lines do not intersect and are not coplanar

6. S KEW L INES

7. P ARALLEL P LANES Parallel Planes do not intersect A line and a plane are parallel if they do not intersect

8. T HEOREM 2-1 If two parallel planes are cut by a third plane, then the lines of intersection are parallel. X Y Z n m

9. D EFINITIONS A transversal is a line that intersects two or more coplanar lines in different points. Alternate interior angles are two nonadjacent interior angles on opposite sides of the transversal Same-side interior angles are two interior angles on the same side of the transversal Corresponding angles are two angles in corresponding positions relative to the two lines 1 2 3 4 5 6 7 8

10. The railroad ties are transversals to the tracks. The tracks are parallel. A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angles with special properties.

11. P ARALLEL L INES C UT BY A T RANSVERSAL (Y OUR BIGS AND SMALLS)

12. Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent?  1,  3,  5, and  7 all measure 150°.  2,  4,  6, and  8 all measure 30°.

13. If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines.

14. PROPERTIES OF TRANSVERSALS TO PARALLEL LINES If two parallel lines are intersected by a transversal, the acute angles that are formed are all congruent, the obtuse angles are all congruent, and any acute angle is supplementary to any obtuse angle. If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90° angles.

15. The symbol for parallel is ||. The symbol for perpendicular is . Writing Math

16. In the figure, line l || line m. Find the measure of the angle. 44 m  4 = 124° All obtuse angles in the figure are congruent.

17. In the figure, line l || line m. Find the measure of the angle. 22  2 is supplementary to the angle 124°. m  2 + 124° = 180° –124° m  2 = 56°

18. In the figure, line l || line m. Find the measure of the angle. 66 All acute angles in the figure are congruent. m  6 = 56°

19. In the figure, line n || line m. Find the measure of the angle. 77 All obtuse angles in the figure are congruent m  7 = 144° 1 144° 3 4 5 6 7 8 m n

20. In the figure, line n || line m. Find the measure of the angle. 1 144° 3 4 5 6 7 8 m n 55  5 is supplementary to the angle 144°. m  5 + 144° = 180° –144° m  5 = 36°

21. Lesson Quiz In the figure a || b. 1. Name the angles congruent to  3. 2. Name all the angles supplementary to  6. 3. If m  1 = 105° what is m  3? 4. If m  5 = 120° what is m  2?  1,  5,  7  1,  3,  5,  7 105° 60°

22. H OMEWORK Worksheet, Parallel Lines #1