1. 3-1 Lines and Angles Geometry

2. LINES AND ANGLES

3. Warm Up 2) The soccer team scored 3 goals in each of their first two games, 7 goals in the next game, and 2 goals in each of the last four games. What was the average (mean) number of goals the team scored per game?

4. Warm Up 9 = = = = = Solve the equation: -0.8 -20

5. MCC7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi- step problem to write and solve simple equations for an unknown angle in a figure.

6. Formative

7. Essential Questions How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems?

8. PARALLEL LINES Lines that do not intersect Notation: l | | m AB | | CD l m A B C D

9. Examples of Parallel Lines Opposite sides of windows, desks, etc. Parking spaces in parking lots Parallel Parking Streets in a city block

10. PERPENDICULAR LINES Lines that intersect to form a right angle Notation: m  n Key Fact: 4 right angles are formed. m n

11. Ex. of Perpendicular Lines

12. any angle less than 90 º Acute Angle –

13. a 90 º angle Right Angle –

14. any angle larger than 90 º Obtuse Angle -

15. angles that add up to 90 º Complementary Angles –

16. angles that add up to 180 º Supplementary Angles –

17. Adjacent Angles - angles that share a common vertex and ray…angles that are back to back. *Vertex – the “corner” of the angle *Ray – a line that has an endpoint on one end and goes on forever in the other direction.

18. Congruent Angles – Angles with equal measurement  A ≅  B denotes that  A is congruent to  B.

19. Transversal - t a line that intersects a set of parallel lines

20. Vertical Angles Two angles that are opposite angles at intersecting lines. Vertical angles are congruent angles. 12 3 4 t 1   41   4  2   3

21. Vertical Angles Find the measures of the missing angles 125  ? ? 55  t 125 

22. Two adjacent angles that form a line. They are supplementary. (angle sum = 180  ) 12 3 4 5 6 78 t Linear Pair  5+  6=180  6+  8=180  8+  7=180  7+  5=180  1+  2=180  2+  4=180  4+  3=180  3+  1=180

23. Supplementary Angles/ Linear Pair Find the measures of the missing angles ? 72  ? t 108  180 - 72

24. Corresponding Angles Two angles that occupy corresponding positions when parallel lines are intersected by a transversal…same side of transversal AND same side of own parallel line. Corresponding angles are congruent angles. Top Left t Top Right Bottom Right Bottom Left 1   51   5  2   6  3   7  4   8 1 2 34 5 6 78

25. Corresponding Angles Find the measure of the missing angle 145  ? t 35  145 

26. Alternate Interior Angles Two angles that lie between parallel lines on opposite sides of the transversal. These angles are congruent. t 33   6 44   5 1 2 34 5 6 78

27. Alternate Interior Angles Find the measure of the missing angle 82  ? t 98  82 

28. Alternate Exterior Angles Two angles that lie outside parallel lines on opposite sides of the transversal. They are congruent. t 22   7 11   8 1 2 34 5 6 78

29. Alternate Exterior Angles Find the measure of the missing angle 120  ? t 60  120 

30. Same Side Interior Angles Two angles that lie between parallel lines on the same sides of the transversal. These angles are supplementary. t 33 +  5 = 180 44 +  6 = 180 1 2 34 5 6 78 *Also known as Consecutive Interior Angles

31. Same Side Interior Angles Find the measure of the missing angle ? t 135  45  180 - 135

32. Same Side Exterior Angles Two angles that lie outside parallel lines on the same side of the transversal. These angles are supplementary. t  1 +  7 = 180  2 +  8 = 180 1 2 34 5 6 78 *Also known as Consecutive Exterior Angles

33. Same Side Exterior Angles Find the measure of the missing angle ? t 135  45  180 - 135

34. 1,54,82,63,7 5,43,6 2,71,8 4,63,5 2,81,7

35. equivalent supplementary

36. 112 º 68 º 112 º 68 º 112 º

37. Closing What is a transversal? Name the types of equivalent angles. Name the types of supplementary angles.