2. C. N. Colón Geometry St. Barnabas HS Bronx, NY Rays and Angles Ch. 1.5 and 1.6

3. A RAY consists of a point on a line and all points on one side of the point. K A D ● ● This ray can be called AK or AD The beginning of the name is the endpoint, A.

4. Opposite rays are two rays of the same line with a common endpoint and no other points in common RAY C●C● T●T● A

5. Oh, Mrs. C, you are tooooooo funny!

6. This is an angle

7. A n angle is a set of points that is the union of two rays having the same endpoint A n Side Vertex D●D● E●E● There are several ways to name this angle: A DAE EAD n

8. In this case there is no confusion you name an angle by the vertex. A A

9. obtuse angle: greater than 90° acute angle: less than 90°

10. A B C D How many angles do you see? A – 1 B – 2 C – 3 D – Huh?

11. Degrees were developed by the Babylonians thousands of years ago. They divided a circle into 360 parts and called each part one degree.

12. The symbol for degrees, as you probably already know, is a small superscript circle. 45°37°112°

14. This is an acute angle and it measures 62º

15. This is an obtuse angle and it measures 128º

16. A: 180B: 125C: 50D: 25

17. Angles are congruent if they have the same measure. A B

18. If point S is in the interior (middle) of angle PQR, then the measure of PQS + measure of SQR = measure of PQR P Q R S

19. P Q R S The bisector of an angle is a ray whose endpoint is the vertex of the angle, and that divides the angle into two congruent angles. PQS = SQR ~

20. Complementary angles are two angles that total 90 degrees 30º and ___ 27º and ___ 12º and ___ 63º 60º 78º

21. Supplementary angles are two angles that total 180 degrees 25º and ___ 67º and ___ 124º and ___ 155º 56º 113º

22. AngleComplementSupplement 28º 49º 67º 100º 147º

23. AngleComplementSupplement 28º62º 49º 67º 100º 147

24. AngleComplementSupplement 28º62º152º 49º 67º 100º 147º

25. AngleComplementSupplement 28º62º152º 49º41º 67º 100º 147º

26. AngleComplementSupplement 28º62º152º 49º41º131º 67º 100º 147º

27. AngleComplementSupplement 28º62º152º 49º41º131º 67º23º 100º 147º

28. AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100º 147º

29. AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100ºnone 147º

30. AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100ºnone80º 147º

31. AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100ºnone80º 147ºnone

32. AngleComplementSupplement 28º62º152º 49º41º131º 67º23º113º 100ºnone80º 147ºnone33º

33. Linear angles are two angles that share a side and make a line. Linear angles total 180°

34. Right angles are angles that measure 90°

35. Acute angles angles that measure less than 90°

36. Obtuse angles are angles that measure more than 90° but less than 180°

37. Straight angle is an angle that makes a straight line and measures 180º

38. Perpendicular lines are lines that intersect to form right angles. The distance from any point to a line is the length of the perpendicular from the point to the line.

39. A reflex angle is an angle that measures more than 180°

40. Read p. 14-18, p. 18 # 3-5 (all) Read p. 19-21, p. 21 #3-20 (e)