This document contains lesson materials on lines and angles including: - Solving two equations involving variables w and v - Vocabulary terms related to lines and angles - Identifying different angle relationships (corresponding angles, interior angles, etc.) when lines are cut by a transversal - Worked examples of finding missing angle measures using properties of parallel lines

1. Lesson 8.1 , For use with pages 403-408 Solve the equation. 1. 7 w = 56 2. = 21 v 3

2. Lesson 8.1 , For use with pages 403-408 Solve the equation. 1. 7 w = 56 ANSWER 8 ANSWER 63 2. = 21 v 3

3. Chapter 8.1 Lines and Angles

4. Chapter 8 Section 1 Vocabulary 15-22

5. Essential Questions Why is it important to be able to identify congruent triangles in everyday life? Where in real life can you use the properties of isosceles and equilateral triangles? How are the relationships between lines and planes used in the real world? What areas in the real world are properties of parallel lines important?

6. 1 2 3 4 5 6 7 8 t  4 and  2  3 and  1  5 and  7  6 and  8 Corresponding angles : any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

7. Corresponding Angles Name the angle relationship Are they congruent or supplementary? Find the value of x x t 151  

8. Interior Angles any of the four angles formed in the area between a pair of parallel lines when a third line cuts them t C A B D

9. Interior Angles Name the angle relationship Are they congruent or supplementary? Find the value of x 81  t x supp

10. Exterior Angles an angle formed by a transversal as it cuts one of two lines and situated on the outside of the line t C A B D

11. Alternate Interior Angles  3 and  7  2 and  6 1 2 3 4 5 6 7 8 t When two lines are crossed by another line, the pairs of angles on opposite sides of the transversal but inside the two lines.

12. Alternate Interior Angles Name the angle relationship Are they congruent or supplementary? Find the value of x 126 t x 

13. Alternate Exterior Angles  5 and  1  4 and  8 1 2 3 4 5 6 7 8 t When two lines are crossed by another line, the pairs of angles on opposite sides of the transversal but outside the two lines.

14. Alternate Exterior Angles Name the angle relationship Are they congruent or supplementary? Find the value of x 125  t x  

15. List all pairs of angles that fit the description. Corresponding Alternate Interior Alternate Exterior 1 2 3 4 5 6 7 8 t

16. Find all angle measures 1 67  3 t 113  180 - 67 2 5 6 7 8 67  67  67  113  113  113 

17. Congruent Angles Angles that have the same measure

18. Perpendicular Lines Lines that intersect and form 90 ° angles are called perpendicular lines.

19. Perpendicular Lines These 4 angles are also form VERTICAL and SUPPLEMENTARY angles.

20. Parallel Lines Two lines in the same plane that do not intersect.

21. SOLUTION EXAMPLE 3 Using Parallel Lines Use the diagram to find the angle measure. Definition of supplementary angles 55° 125° 125° 55° 55° 126° 55° a. m 1 b. m 2 a. 1 and 5 are corresponding angles, so they have equal measures. You can find m 5 because it is the supplement of the given angle. m 5 = 55 Subtract 125 from each side. ANSWER m 1 = 55 m 5 + 125 = 180

22. EXAMPLE 3 Using Parallel Lines b. 2 and the given angle are alternate exterior angles, so they have equal measures. ANSWER m 2 = 125

23. GUIDED PRACTICE for Example 3 SOLUTION 85° 95° 95° 85° 95° 85° 95° m 2 and the given angle are corresponding angles, so they have equal measures. ANSWER m 2 = 85 9. m 2 Find the angle measure.

24. Assignment: P. 406 #12-23, 28-31